Precalculus Examples

$3 \log_{4} (x) + 2 \log_{4} (x)$

Step 1

Simplify each term.

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Step 1.1

Simplify $3 \log_{4} (x)$ by moving $3$ inside the logarithm.

$\log_{4} (x^{3}) + 2 \log_{4} (x)$

Step 1.2

Simplify $2 \log_{4} (x)$ by moving $2$ inside the logarithm.

$\log_{4} (x^{3}) + \log_{4} (x^{2})$

Step 2

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

$\log_{4} (x^{3} x^{2})$

Step 3

Multiply $x^{3}$ by $x^{2}$ 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.

$\log_{4} (x^{3 + 2})$

Step 3.2

Add $3$ and $2$ .

$\log_{4} (x^{5})$