Precalculus Examples

$4 \log_{x} (8) + 2 \log_{x} (9)$

Step 1

Simplify each term.

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Step 1.1

Simplify $4 \log_{x} (8)$ by moving $4$ inside the logarithm.

$\log_{x} (8^{4}) + 2 \log_{x} (9)$

Step 1.2

Raise $8$ to the power of $4$ .

$\log_{x} (4096) + 2 \log_{x} (9)$

Step 1.3

Simplify $2 \log_{x} (9)$ by moving $2$ inside the logarithm.

$\log_{x} (4096) + \log_{x} (9^{2})$

Step 1.4

Raise $9$ to the power of $2$ .

$\log_{x} (4096) + \log_{x} (81)$

Step 2

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

$\log_{x} (4096 \cdot 81)$

Step 3

Multiply $4096$ by $81$ .

$\log_{x} (331776)$