Definition

Logarithm to exponential form

Algebra • Logarithm • Equations

Formula

lo g_{b} A = c ⟺ A = b^{c}

For

b > 0

b \neq = 1

and

A > 0

lo g_{b} A = c

means exactly

A = b^{c}

. Solving a logarithmic equation therefore begins by rewriting it without the logarithm.

How to use it

Solve

lo g_{3} (2 x - 1) = 2

Step-by-step

1
$2 x - 1 = 3^{2} = 9$
Why: Rewrite the equation without the logarithm.
2
$2 x = 10 \Rightarrow x = 5$
3
$2 x - 1 = 9 > 0$
Why: Confirm the argument is positive, so the root is admissible.

Answer

x = 5

Watch out

The argument must be positive, so a candidate root making it zero or negative is rejected. Note

lo g_{b} A = 1

gives

A = b

; only

lo g_{b} A = 0

gives

A = 1

Also known as

definition of logarithm, log to index form, antilog