The exponential form of a logarithm is a way of rewriting a logarithmic equation as an exponential equation.

General Form

If you have a logarithmic equation:

$$\log_b(x) = y$$

It can be rewritten in exponential form as:

$$b^y = x$$

where:

• ( b ) is the base of the logarithm,
• ( x ) is the result,
• ( y ) is the exponent.

Examples

1. $$\log_2(8) = 3$$

   can be rewritten as:

   $$2^3 = 8$$
2. $$\log_{10}(1000) = 3$$

   is equivalent to:

   $$10^3 = 1000$$

Why Use Exponential Form?

• It helps in solving logarithmic equations.
• It makes it easier to understand the relationship between logarithms and exponents.
• It is useful for converting between exponential and logarithmic functions in algebra and calculus.

Latex

b^y = x \iff log_b​(x)=y