Precalculus Examples

$\frac{7}{2} \cdot \log_{n} (5 y + \frac{4}{7} \cdot \log_{n} (25 y^{2}))$

Step 1

Simplify each term.

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Step 1.1

Simplify $\frac{4}{7} \log_{n} (25 y^{2})$ by moving $\frac{4}{7}$ inside the logarithm.

$\frac{7}{2} \cdot \log_{n} (5 y + \log_{n} ({(25 y^{2})}^{\frac{4}{7}}))$

Step 1.2

Apply the product rule to $25 y^{2}$ .

$\frac{7}{2} \cdot \log_{n} (5 y + \log_{n} (25^{\frac{4}{7}} {(y^{2})}^{\frac{4}{7}}))$

Step 1.3

Multiply the exponents in ${(y^{2})}^{\frac{4}{7}}$ .

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Step 1.3.1

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

$\frac{7}{2} \cdot \log_{n} (5 y + \log_{n} (25^{\frac{4}{7}} y^{2 (\frac{4}{7})}))$

Step 1.3.2

Multiply $2 (\frac{4}{7})$ .

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Step 1.3.2.1

Combine $2$ and $\frac{4}{7}$ .

$\frac{7}{2} \cdot \log_{n} (5 y + \log_{n} (25^{\frac{4}{7}} y^{\frac{2 \cdot 4}{7}}))$

Step 1.3.2.2

Multiply $2$ by $4$ .

$\frac{7}{2} \cdot \log_{n} (5 y + \log_{n} (25^{\frac{4}{7}} y^{\frac{8}{7}}))$

Step 2

Simplify $\frac{7}{2} \log_{n} (5 y + \log_{n} (25^{\frac{4}{7}} y^{\frac{8}{7}}))$ by moving $\frac{7}{2}$ inside the logarithm.

$\log_{n} ({(5 y + \log_{n} (25^{\frac{4}{7}} y^{\frac{8}{7}}))}^{\frac{7}{2}})$