Precalculus Examples

$\frac{1}{5} \cdot (\log (9) p) + \frac{1}{8} \cdot (\log_{9} (q - 2) \log_{9} (t))$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{1}{5} (\log (9) p)$ .

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Step 1.1.1

Reorder $\log (9)$ and $\frac{1}{5}$ .

$\frac{1}{5} \log (9) p + \frac{1}{8} \cdot (\log_{9} (q - 2) \log_{9} (t))$

Step 1.1.2

Simplify $\frac{1}{5} \log (9)$ by moving $\frac{1}{5}$ inside the logarithm.

$\log (9^{\frac{1}{5}}) p + \frac{1}{8} \cdot (\log_{9} (q - 2) \log_{9} (t))$

Step 1.2

Multiply $\frac{1}{8} (\log_{9} (q - 2) \log_{9} (t))$ .

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Step 1.2.1

Reorder $\log_{9} (q - 2)$ and $\frac{1}{8}$ .

$\log (9^{\frac{1}{5}}) p + \frac{1}{8} \log_{9} (q - 2) \log_{9} (t)$

Step 1.2.2

Simplify $\frac{1}{8} \log_{9} (q - 2)$ by moving $\frac{1}{8}$ inside the logarithm.

$\log (9^{\frac{1}{5}}) p + \log_{9} ({(q - 2)}^{\frac{1}{8}}) \log_{9} (t)$

Step 2

Reorder factors in $\log (9^{\frac{1}{5}}) p + \log_{9} ({(q - 2)}^{\frac{1}{8}}) \log_{9} (t)$ .

$p \log (9^{\frac{1}{5}}) + \log_{9} ({(q - 2)}^{\frac{1}{8}}) \log_{9} (t)$