Precalculus Examples

$\log_{8} (x) + \log_{8} (y) + 6 \log (8) z$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{8} (x y) + 6 \log (8) z$

Step 2

Simplify each term.

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Step 2.1

Simplify $6 \log (8)$ by moving $6$ inside the logarithm.

$\log_{8} (x y) + \log (8^{6}) z$

Step 2.2

Raise $8$ to the power of $6$ .

$\log_{8} (x y) + \log (262144) z$

Step 3

Reorder factors in $\log_{8} (x y) + \log (262144) z$ .

$\log_{8} (x y) + z \log (262144)$