Precalculus Examples

$7 \log_{b} (x) + 6 \log_{b} (x)$

Step 1

Simplify each term.

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Step 1.1

Simplify $7 \log_{b} (x)$ by moving $7$ inside the logarithm.

$\log_{b} (x^{7}) + 6 \log_{b} (x)$

Step 1.2

Simplify $6 \log_{b} (x)$ by moving $6$ inside the logarithm.

$\log_{b} (x^{7}) + \log_{b} (x^{6})$

Step 2

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

$\log_{b} (x^{7} x^{6})$

Step 3

Multiply $x^{7}$ by $x^{6}$ by adding the exponents.

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Step 3.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\log_{b} (x^{7 + 6})$

Step 3.2

Add $7$ and $6$ .

$\log_{b} (x^{13})$