# Convert Exponentials and Logarithms | Relationship between Exponentials and Logarithms

Are you looking for ways on how to convert from Exponential Form to Logarithmic Form? Then, don’t panic as we will discuss how to change Exponential Form to Logarithmic Form or Vice Versa. Get to know the Definitions of Exponential and Logarithmic Forms. Find Solved Examples on Converting between Exponential and Logarithmic Forms and learn the entire procedure.

### Logarithmic Form – Definition

Logarithmic Functions are inverse of Exponential Functions. It tells us how many times we need to multiply a number to get another number. To give us the ability to solve the problem x = by for y

For x>0, b>0 b≠ 1, y = logb x is equivalent to by = x

Example: When asked how many times we’ll need to multiply 2 in order to get 32, the answer is the logarithm 5.

### Exponential Form – Definition

Exponents are when a number is raised to a certain power that tells you how many times to repeat the multiplication of a number by itself.

by = x

## How to Convert from Exponential Form to Logarithmic Form?

To convert from exponential form to logarithmic form, identify the base of the exponential equation
and move the base to the other side of the equal to sign, and add the word “log”. Do not change anything
but the base, the other numbers or variables will not change sides.

Consider the equation by = x

The equation y = logb x is said to be the Logarithmic Form

by = x is said to be Exponential Form

Two Equations are different ways of writing the same thing.

### Solved Examples on Converting Between Exponential Form to Logarithmic Form

1. Convert the 103 = 1000 Exponential Form to Logarithmic Form?

Solution:

103 = 1000

log101000 = 3

In this example, the base is 10 and the base moved from the left side of the exponential equation to the right side of the logarithmic equation, and the word “log” was added.

2. Write the Exponential Equation 3x = 27 in Logarithmic Form?

Solution:

3x = 27

In this example, the base is 3 and the base moved from the left side of the exponential equation to the right side of the logarithmic equation, and the word “log” was added.

x = log327

= log333

= 3log33

= 3.1

= 3

3. Write the Exponential Equation  6y = 98 in Logarithmic Form?

Solution:

Given Equation is 6y = 98

In this example, the base is 6 and the base moved from the left side of the exponential equation to the right side of the logarithmic equation, and the word “log” was added.

y = log6 98

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