Precalculus Examples

{log}_{3} (20)

$\log_{3} (20)$

Step 1

The change of base rule can be used if

a

$a$ and

b

$b$ are greater than

0

$0$ and not equal to

1

$1$ , and

x

$x$ is greater than

0

$0$ .

{log}_{a} (x) = \frac{{log}_{b} (x)}{{log}_{b} (a)}

$\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}$

Step 2

Substitute in values for the variables in the change of base formula, using

b = 10

$b = 10$ .

\frac{log (20)}{log (3)}

$\frac{\log (20)}{\log (3)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

\frac{log (20)}{log (3)}

$\frac{\log (20)}{\log (3)}$

Decimal Form:

2.72683302 \dots

$2.72683302 \dots$