Precalculus Examples

$4^{\log_{4} (9)} + \log_{3} ({(3)}^{- 3})$

Step 1

Simplify each term.

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Step 1.1

Exponentiation and log are inverse functions.

$9 + \log_{3} ({(3)}^{- 3})$

Step 1.2

Use logarithm rules to move $- 3$ out of the exponent.

$9 - 3 \log_{3} (3)$

Step 1.3

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

$9 - 3 \cdot 1$

Step 1.4

Multiply $- 3$ by $1$ .

$9 - 3$

Step 2

Subtract $3$ from $9$ .

$6$