Precalculus Examples

$\log_{24} (288)$

Step 1

Rewrite $\log_{24} (288)$ as $\log_{24} (2^{5} \cdot 3^{2})$ .

$\log_{24} (2^{5} \cdot 3^{2})$

Step 2

Rewrite $\log_{24} (2^{5} \cdot 3^{2})$ as $\log_{24} (2^{5}) + \log_{24} (3^{2})$ .

$\log_{24} (2^{5}) + \log_{24} (3^{2})$

Step 3

Simplify each term.

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Step 3.1

Expand $\log_{24} (2^{5})$ by moving $5$ outside the logarithm.

$5 \log_{24} (2) + \log_{24} (3^{2})$

Step 3.2

Expand $\log_{24} (3^{2})$ by moving $2$ outside the logarithm.

$5 \log_{24} (2) + 2 \log_{24} (3)$