Precalculus Examples

$\frac{1}{7} \cdot (\log_{7} (z) + 4 \log_{7} (y))$

Step 1

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

$\frac{1}{7} \cdot (\log_{7} (z) + \log_{7} (y^{4}))$

Step 2

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

$\frac{1}{7} \cdot \log_{7} (z y^{4})$

Step 3

Simplify $\frac{1}{7} \log_{7} (z y^{4})$ by moving $\frac{1}{7}$ inside the logarithm.

$\log_{7} ({(z y^{4})}^{\frac{1}{7}})$

Step 4

Apply the product rule to $z y^{4}$ .

$\log_{7} (z^{\frac{1}{7}} {(y^{4})}^{\frac{1}{7}})$

Step 5

Multiply the exponents in ${(y^{4})}^{\frac{1}{7}}$ .

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Step 5.1

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

$\log_{7} (z^{\frac{1}{7}} y^{4 (\frac{1}{7})})$

Step 5.2

Combine $4$ and $\frac{1}{7}$ .

$\log_{7} (z^{\frac{1}{7}} y^{\frac{4}{7}})$