Precalculus Examples

$\log_{15} (\log_{3} ({(3)}^{15})) = x$

Step 1

Rewrite the equation as $x = \log_{15} (\log_{3} (3^{15}))$ .

$x = \log_{15} (\log_{3} (3^{15}))$

Step 2

Simplify $\log_{15} (\log_{3} (3^{15}))$ .

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Step 2.1

Use logarithm rules to move $15$ out of the exponent.

$x = \log_{15} (15 \log_{3} (3))$

Step 2.2

Logarithm base $3$ of $3$ is $1$ .

$x = \log_{15} (15 \cdot 1)$

Step 2.3

Multiply $15$ by $1$ .

$x = \log_{15} (15)$

Step 2.4

Logarithm base $15$ of $15$ is $1$ .

$x = 1$