Precalculus Examples

$10^{4 (\log (x^{2}) - \log (y))}$

Step 1

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

$10^{4 \log (\frac{x^{2}}{y})}$

Step 2

Simplify $4 \log (\frac{x^{2}}{y})$ by moving $4$ inside the logarithm.

$10^{\log ({(\frac{x^{2}}{y})}^{4})}$

Step 3

Exponentiation and log are inverse functions.

${(\frac{x^{2}}{y})}^{4}$

Step 4

Apply the product rule to $\frac{x^{2}}{y}$ .

$\frac{{(x^{2})}^{4}}{y^{4}}$

Step 5

Multiply the exponents in ${(x^{2})}^{4}$ .

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Step 5.1

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

$\frac{x^{2 \cdot 4}}{y^{4}}$

Step 5.2

Multiply $2$ by $4$ .

$\frac{x^{8}}{y^{4}}$