# Logarithm Calculator

Logarithm Calculator is a free online tool that displays the logarithm of the given number. BYJU’S online logarithm calculator tool makes the calculation faster, and it displays the logarithm value in a fraction of seconds.

## How to Use the Logarithm Calculator?

The procedure to use the log calculator is as follows:
Step 1: Enter the base value and the number in the respective input field
Step 2: Now click the button “Submit” to get the value
Step 3: Finally, the logarithm value for the given number will be displayed in the new window

### What is Meant by Logarithm?

In Mathematics, the logarithm is considered as a convenient method to express the large numbers. The logarithm is defined as a power to which some number is raised in order to get some other numbers. The logarithmic function is generally defined as follows:
For x > 0 , a > 0, and a≠1,
y= loga x if and only if x = ay
Then the logarithmic function is given by
f(x) = loga x
There are two different types of logarithmic functions. They are:
1. Common Logarithmic Function (whose base is 10)
2. Natural Logarithmic Function (Whose base is e)

## Examples Based On Log Calculator

Example 1:
Solve for x: 4 + log3(7x) = 10
Solution:
4 + log3(7x) = 10
Subtracting 4 from both sides, we get;
4 + log3(7x) – 4 = 10 – 4
log3(7x) = 6
7x = 36
7x = 729
x = 729/7
Example 2:
Solve:

$$\begin{array}{l}\log \sqrt{x+4}-\log \sqrt{x-4}=\log 12-\log 4\end{array}$$

Solution:
Given,

$$\begin{array}{l}\log \sqrt{x+4}-\log \sqrt{x-4}=\log 12-\log 4\end{array}$$

By applying the quotient rule,

$$\begin{array}{l}\log \frac{\sqrt{x+4}}{\sqrt{x-4}}=\log \frac{12}{4}\end{array}$$

Now, taking the log out,

$$\begin{array}{l}\frac{\sqrt{x+4}}{\sqrt{x-4}}=3\end{array}$$

Squaring on both sides,
(x + 4)/(x – 4) = 32
x + 4 = 9(x – 4)
x + 4 = 9x-36
8x = 40
x = 5