# Log Calculator – Logarithm Calculator Online

Use this Log Calculator for any type of logarithmic calculation. Also, it gives fast and accurate answers. Even more, the Logarithm calculator is absolutely free to use.

log

Related ### Logarithm Definition

The logarithm can be defined as the inverse function to the exponent. The concept of the logarithm is used in various fields. In mathematics and science, you find the most. Almost every branch of science implements a logarithm.

Let ‘b’ be raised to the power of x is equal to y. The mathematical equation for it is:

bx = y

Then, the logarithm of y with base b. It will be equal to x. The mathematical equation for it is

logb(y) = x

##### Example 1

We know that 23 = 8. Then the

log2(8) = 3

Here, the base is 2. So, the log of 8 with base 2 is 3. Do it in the logarithm calculator.

##### Example 2

We know that 25 = 32. Then the

log2(32) = 5

Here, the base is 2. So, the log of 32 with base 2 is 5.

This is how the log calculator works. There are some logarithmic rules. We will also see them. The log tells the number of common occurrences. Occurrences of the factor in repeated products.

##### Example 3

100 = 10 x 10 = 102. Therefore, logarithm base 10 of 100 is 2. Consequently,

log10(100) = 2

##### Example 4

10000 = 10 x 10 x 10 x 10 = 104. Therefore, logarithm base 10 of 10000 is 4. Consequently,

log10(10000) = 4

### History of Logarithm

John Napier founded the concept of Logarithm. It was an efficient way to simply big numbers. Also, made the calculation much easier. It was accepted by all professions. As it simplified various calculations. Time elapsed was very less. Also, you can find out accurate results. Now, you have to spend a lesser amount of time. Use our log calculator to find the logarithm of any number.

### Applications of Logarithm / Log Calculator

As we have learned about what is logarithm, how the logarithm calculator works. So, now it’s time to look over some applications. Why logarithm is used? The following are the main reasons:

1. Logarithms can be best used for representing very big and very small numbers. This simplification makes the calculation easier. Furthermore, scientific quantities like pH implement this concept.
2. Physical effects like cooling down of hot bodies and damping of the oscillator are best represented using logarithmic decrement.

### Logarithm rules

1. Logarithm product rule

logb (x ∙ y) = logb (x) + logb (y)

2. Logarithm quotient rule

logb (x / y) = logb (x) – logb (y)

3. Logarithm power rule

logb (xy) = y ∙ logb (x)

4. Logarithm base interchange rule

logb (c) = 1 / logc (b)

5. Logarithm base change rule

logb (x) = logc (x) / logc (b)

6. Logarithmic derivative

f (y) = logb (y) ⇒ f ‘ (y) = 1 / (y ln(b))

7. Logarithmic Integral

∫ logb(y) dx = y ∙ ( logb(y) – 1 / ln(b) ) + C

8. The logarithm of negative numbers

The logarithm of a negative number is undefined. The graph of the log always goes in a positive direction.

9. Logarithm of zero

logb (0) = undefined

10. Logarithm of 1

The logb (1) = 0

11. Logarithm of base

The log of the base will be logb (b) = 1

12. Logarithm of Infinity

lim logb (x) = ∞ (Infinite), when x → ∞ (Infinite)

### How to use the Log Calculator?

A logarithm calculator is an online tool. You can use it just by opening its website. In any web browser. In any internet-accessible device. Anytime and anywhere. Even more, you can get rapid and accurate results. Follow these steps one by one. It will guide you through finding the log of a number.