Basic Math Examples

$3 \log_{(3)} (5)$

Step 1

Simplify

$3 \log_{3} (5)$ by moving

$3$ inside the logarithm.

$\log_{3} (5^{3})$

Step 2

Raise

$5$ to the power of

$3$ .

$\log_{3} (125)$

Step 3

Rewrite

$\log_{3} (125)$ using the change of base formula.

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Step 3.1

The change of base rule can be used if

$a$ and

$b$ are greater than

$0$ and not equal to

$1$ , and

$x$ is greater than

$0$ .

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

Step 3.2

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

$b = 10$ .

$\frac{\log (125)}{\log (3)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (125)}{\log (3)}$

Decimal Form:

$4.39492056 \dots$