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:
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
- Properties of logarithms
- Solved logarithm exercises
- What is the base of a logarithm?
- How to solve an equation with logarithms?
- Calculate logarithms in Excel
- What are logarithms for?
- How the logarithm calculator works
- How to solve logarithms with the scientific calculator
Things you should know about logarithms
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:
- The logarithm of a division is equal to the subtraction of the logarithms of the dividend minus the logarithm of the divisor:
- The logarithm of a power is equivalent to the multiplication of the exponent by the logarithm of the base of the power:
- The logarithm of a root can be expressed as follows:
- 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:
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:
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
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.