Logarithm Calculator

Calculate logarithms online without the need for calculators and formulas is possible thanks to our tool. You only have to enter the base value of the logarithm and the number on which you want to apply the operation.

Remember that theory tells us that the logarithm of a numberin a given base, is the exponent to which we must raise the base to obtain the same number. This theoretical statement is reflected in the following mathematical formula:

Logarithm Calculator

Having seen the theory a little bit in detail, you can move on to calculate the logarithm online with our tool:

If you prefer, you can also calculate neperian logarithms which are those in which the base corresponds to the value of the number 'e'. Of course, we also have a section dedicated to the operation of the antilogarithmthe inverse operation to the log of a number.

Things you should know about logarithms

Logarithm Calculator

The logarithm function, by its definition, entails a series of conditions that we must be aware of in order to avoid calculation errors:

  • It is not possible to calculate the logarithm in negative basis of a number.
  • There is no logarithm of a negative number or the logarithm of zero.
  • The logarithm of the number 1 is equal to zero: logx1 = 0
  • The logarithm in base x of the number x is equal to 1: logxx = 1
  • The logarithm in base x of a power in base x is equal to the exponent of the power: logxxn = n

Properties of logarithms

In addition to the above, performing operations with logarithms is subject to a series of properties that we mention below. When you are faced with logarithm exercises it is very important to keep them in mind as they can make it much easier for you to find the result:

  • The logarithm of a product is equal to the sum of the logarithms of the multiplication factors:

Product of logarithms

  • The logarithm of a division is equal to the subtraction of the logarithms of the dividend minus the logarithm of the divisor:

Division of logarithms

  • The logarithm of a power is equivalent to the multiplication of the exponent by the logarithm of the base of the power:

Logarithm of a power

  • The logarithm of a root can be expressed as follows:

Logarithm of a root

  • To perform a change of baseIf we are using the new base, we have to divide the quotient of the logarithm of the number in the new base by the logarithm of the starting base:

Change of base

Solved logarithm exercises

To help you understand how to solve logarithms, let's look at some common examples.

What is the logarithm of 2

Whenever the base of the logarithm is not specified, we will take base 10 as the typical value:

log(2) = x → 2 = 10x

By what number do we have to raise to 10 to get 2? The answer is 0.3.

Therefore, log(2) = 0.3

What is the logarithm of 50

In case we still have doubts about how to calculate logarithms, let's look at another example in which we are asked to calculate the log of 50. Again, as no base is specified, we will take 10 as a typical value:

log(50) = x → 50 = 10x

At a glance we know that x shall be a value between 1 and 2 since 101= 10 (we fall short) and 102 = 100 (we went over).

In this case, the answer is that log(50) = 1.70

If you have doubts or want to solve a particular log, write a comment and we will help you with the exercise.

What is the base of a logarithm?

If we are asked to calculate the base of a logarithmIf we do not see it again, we have to go back to the formula we saw at the beginning. Let's look at it again:

loga(b) = x → b = ax

The base value of the logarithm is a, but is it how to get it if we are given how much the logarithm of a number is worth? To understand it better, let's see it with a practical example:

loga(8) = 3 → 8 = a3

To get the base, we have to find a number that raised to the cube gives us 8. This is a simple operation since we know that to clear a power, the operation passes to the opposite side in the form of a root. That is to say:

a = ∛8 = 2

We have calculated the cube root of 8 and the result is 2. Therefore, the base of our logarithm is 2.

In case it is not clear, we are going to see another exercise in which we are asked to find out what is the base of the logarithm:

loga(16) = 2 → 16 = a2

In this case, the solution is simple since we will only have to calculate the square root of 16:

a = √16 = 4

Any questions? Ask us!

How to solve an equation with logarithms?

To solve an equation with logarithms you have to apply the properties and the formula of the definition of logarithms that we have seen above. Expressing a logarithm as a power will help you to do many simple exercises but for the more complicated ones you will also have to make use of the properties.

For example, let's solve the following equation with logarithms:

log x + log 4 = log 32

The sum of two logarithms can be expressed as a multiplication. Therefore, the above equation looks like this

log4x = log32

We clear and we are left with the following:

4x = 32

x = 8

Logically, there are equations with logarithms that are much more complex to solve and their resolution will not be as obvious as in the previous example.

Calculate logarithms in Excel

If you want to create your own logarithm calculator using ExcelIn the LOG function, you have to use the LOG function that will allow you to calculate logarithms of a number in any base.

To use this formula, choose a cell in your spreadsheet and type this function:

=LOG(A1;B2)

You should keep in mind that:

  • A1 is the cell coordinate of the cell in which the number for which you want calculate its logarithm.
  • B2 is the base of the logarithm.

After writing the formula to solve logarithms in ExcelIf you have a new calculation, you will get the automated calculation to use it whenever you want.

What are logarithms for?

Logarithms were born as a a tool to facilitate the resolution of arithmetic and geometric exercises.This way we avoid having to do complex multiplications and divisions. As we have seen before, the logarithm is able to transform multiplications into additions and divisions into subtractions.

But,what logarithms are for? There is no single answer to this question because logarithms are used in many fields and are therefore used in economics, banking, statistics, advertising, medicine, psychology, physics, engineering, biology, geology, astronomy, chemistry, surveying, aviation, music and a long etcetera.

For this very reason, it is very important for you to know how to solve logarithms and understand its properties very well.

How the logarithm calculator works

In this video we have recorded how to use our logarithm calculator so that you have no doubt about how to solve this operation using our tool.

For solve logarithms online just enter the value of the base and enter the number. Then click the calculate button to get the log(x).

If you still have doubts when calculating logarithms, leave us a comment and we will try to help you as soon as possible. We hope that our page to solve logarithms has been of help to you.

How to solve logarithms with the scientific calculator

Logarithm Calculator

If you have a scientific calculator at hand, you can solve logarithms very simply.

We have taken as an example a Casio scientific calculator but the truth is that most brands and simple calculators have a key dedicated to calculate logarithms.

You will be able to identify it very easily because you will see the letters "log" engraved on its surface so you only have to press it, write the number of which you want to obtain its logarithm and press the equal key (=) to know the result.

Note that by default, the logarithm calculator performs the operation with the log in base 10 but if we need to change it, we can also do it without any problem.

35 thoughts on “Calculadora de logaritmos”

  1. Please I can not solve a logarithmic equation to find x and it is the following, thank you infinitely for your answer:

    2 logx=log2+log〖(3x-4)〗

    Reply
    • Hello Luz,

      We cannot solve the exercise for you as this is not our purpose but we can help you to do the logarithmic equation.

      The first thing to keep in mind is that you have to clear the x and to do so, you must take into account the properties of logarithms:

      First property

      log M - log N = log (M/N)

      Second property

      n-log P = log Pⁿ

      By applying them to your logarithmic equation, you can solve it with relative ease. If you still have problems, tell us where you are stuck and we will help you.

      Greetings!

    • Hello Juan,

      We do not usually solve the exercises since that is not our purpose but I am going to give you hints to solve it. What you have to do is to express the cube root as a power and use the properties of logarithms.

      Then you will see that ln(∛e) = 1/3ln(e)

      That's easy enough to solve.

      Greetings!

  2. hello, I would like you to help me to solve this logarithm(the log(x2-1) means that x is squared).
    log(x+1)-log(x2-1)=log(x+√ 7)+log(x-√ 7)

    Reply
    • Hi Javi,

      What you want to calculate is a logarithm in base 4 whose result is -2.

      You can check it yourself by solving the basic rule of logarithms

      b = ax

      In this case:

      0,0625 = 4-2

  3. I NEED HELP FAST WITH THIS!!!!!!!!!!!
    Could you please tell me how to do it?

    log5 (2x+5) - log 5 (x+3)

    2. log3 (x+2) = log3 729

    log 2 (x-1) + log 2 (3x+1) =6

    4. log x - log 9+2 =0

    Reply
  4. excellent site, clear and concise work, without so many useless technical terms, thank you very much, keep up the good work.

    Reply
    • Thank you very much Daniel,

      The purpose of our calculators is exactly what you are talking about: to find the result you are looking for in a simple way.

      We hope to see you more soon and if you have any questions about logarithms ask us with confidence that we will try to help you as soon as possible.

      Greetings!

    • Hello Sofia,

      It is possible to calculate logarithms with decimal base but the decimal separator we use in Spain is the ,

      . we use it as a separator of thousands.

      Greetings!

      Greetings!

  5. Hi, Your calculator is really fantastic. Before to solve logarithms I put in excel the base and the exponents 1.1, 1.2, 1.3, 1.4... and performed the operation to find the exponent that squared; with your calculator I do it in a second! I only have one question: if I wanted to solve how to solve this mechanically for example: log15X=150? how could I solve it?

    Reply
    • Hello Tonatiuh,

      To solve logarithms there is no choice but to use the traditional method with the formula. There are some logarithmic bases like 2 or 10 that allow you to solve logarithms mentally with ease but others require using the formula or our calculator to save time.

      Greetings and thank you very much for the comment, we are glad you like it.

    • Hello Francisco,

      It is not clear to me if you have to calculate the logarithm since it seems that what you have sent us is a system of one equation with one unknown.

      Let us know if you are asked to solve the system using logarithms and we will guide you to solve the exercise.

      Greetings!

    • Hello Mathias,

      I don't understand what the {x+1} refers to. How is it integrated in the logarithm exercise? Can you give us the complete statement of what you are asked so we can help you solve it?

      Greetings!

  6. Hello, good afternoon.
    A help please, I have (log in base (2401/16) of (1/128) )raised to -1 : log in base 512 of (49/4) I have to solve using properties but I don't get it.

    Reply
    • Hello Pablo,

      If you have it raised to -1, you can start solving the exercise using the property of the logarithm of a power.

      If working with fractions makes your calculations difficult, you can always convert it to a decimal number.

      Greetings!

    • Hello Luis,

      We solve the first one since the second one would be done exactly the same. You only have to apply the logarithm formula which is the following:

      logab = x ↔ b = ax

      You start from the statement x=29 which is the second part of the logarithm formula and therefore:

      b = x
      a = 2
      x = 9

      Now you just have to substitute in logarithmic form of the equation:

      log2x = 9

      Do you dare to make the next one?

      Greetings!

  7. Hello Oriana,

    We will do one of the examples you send us since our job is not to solve exercises. The other two would be done in the same way.

    2logx - log(x+6) = 0

    What we do is to reorder the elements on both sides of the equality and we are left with:

    2logx = log(x+6)

    By the properties of logarithms, we have that:

    logx2 = log(x+6)

    Now we can clear the logarithms and we are left with the equation:

    x2 = x + 6

    We regroup everything and obtain the following second degree equation:

    x2 - x - 6 = 0

    When we solve it (here you can do it: https://www.calculadoraconversor.com/calculadora-ecuacion-segundo-grado/) we get that x = 3 and x = -2

    If you have any specific questions for the other two, let us know.

    Greetings!

    Reply
  8. Hello good afternoon, I don't know how to do this logarithm exercise Log(3x^2+ 16x) - Log(x+36) - 1= 0 I know I have to divide 3x^2+ 16x/x+36 but then I don't know how to continue.

    Reply
    • Hello,

      You have to eliminate the denominator of the equation by factoring and solve the third degree equation that you will be left with.

      Greetings!

    • Hello Ana,

      What exactly is your problem? Note that the logarithm of a fraction can be expressed as Log2(0.25).

      All we have done is to convert the fraction to decimal and solve it.

      Greetings!

    • Hi Armando, you just have to apply the properties of logarithms to solve this exercise.

      log32 / log2 = log32 - log2

      You just have to solve each logarithm individually, perform the subtraction and you will get the result you are looking for.

      Greetings!

    • Hi Jc,

      Your exercise is quite simple. The first thing we do is to leave out of the equation only the logarithm:

      Log (x-2) = 8/x

      Now we use the properties of logarithms to solve:

      (x-2) = 10(8/x)

      And now you simply have to clear the value of X.

      Greetings!

  9. Hello, I need some clue to be able to solve the following exercise, since I can not find the rules that I must apply, I would greatly appreciate some kind of clue, the exercise is as follows:

    simplify the following expression: x raised to 1 divided by the logarithm in base a of x

    the most I get is to reduce it to 1 match of x raised to the logarithm in base a of x

    thank you very much.

    Reply

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