# Logarithm Equation Calculator

## Calculator Use

This calculator will solve the basic log equation log_{b}x = y for any one of the variables as long as you enter the other two.

The logarithmic equation is solved using the logarithmic function:

which is equivalently

## How to solve the logarithmic equation

If we have the equation used in the Logarithm Equation Calculator

We can say the following is also true

Using the logarithmic function where

We can rewrite our equation (2) to solve for x

Solving for b in equation (3) we have

Solving for y in equation (3)

take the log of both sides:

Using logarithmic identity we rewrite the equation:

Dividing both sides by log b:

Note that writing log without the subscript for the base it is assumed to be log base 10 as in log_{10}.

### Example 1: Solve for y in the following logarithmic equation

If we have

then it is also true that

Using the logarithmic function we can rewrite the left side of the equation and we get

To solve for y, first take the log of both sides:

By the identity log x^{y} = y · log x we get:

Dividing both sides by log 3:

Using a calculator we can find that log 5 ≈ 0.69897 and log 3 ≈ 0.4771 2 then our equation becomes:

Therefore, putting y back into our original equation

### Example 2: Solve for b in the following logarithmic equation

If we have

then it is also true that

Using the logarithmic function we can rewrite the left side of the equation and we get

Solving for b by taking the 2nd root of both sides of the equation

Therefore, putting b back into our original equation