Trigonometry Examples

$\log_{6} (\frac{24}{5})$

Step 1

Rewrite $\log_{6} (\frac{24}{5})$ as $\log_{6} (24) - \log_{6} (5)$ .

$\log_{6} (24) - \log_{6} (5)$

Step 2

Simplify each term.

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Step 2.1

Rewrite $\log_{6} (24)$ as $\log_{6} (2^{3} \cdot 3)$ .

$\log_{6} (2^{3} \cdot 3) - \log_{6} (5)$

Step 2.2

Rewrite $\log_{6} (2^{3} \cdot 3)$ as $\log_{6} (2^{3}) + \log_{6} (3)$ .

$\log_{6} (2^{3}) + \log_{6} (3) - \log_{6} (5)$

Step 2.3

Expand $\log_{6} (2^{3})$ by moving $3$ outside the logarithm.

$3 \log_{6} (2) + \log_{6} (3) - \log_{6} (5)$