Algebra Examples

$7 \cdot \log_{4} (u) - 3 \cdot \log_{4} (v^{2})$

Step 1

Simplify each term.

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Step 1.1

Simplify $7 \log_{4} (u)$ by moving $7$ inside the logarithm.

$\log_{4} (u^{7}) - 3 \cdot \log_{4} (v^{2})$

Step 1.2

Simplify $- 3 \log_{4} (v^{2})$ by moving $3$ inside the logarithm.

$\log_{4} (u^{7}) - \log_{4} ({(v^{2})}^{3})$

Step 1.3

Multiply the exponents in ${(v^{2})}^{3}$ .

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Step 1.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log_{4} (u^{7}) - \log_{4} (v^{2 \cdot 3})$

Step 1.3.2

Multiply $2$ by $3$ .

$\log_{4} (u^{7}) - \log_{4} (v^{6})$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{4} (\frac{u^{7}}{v^{6}})$