Precalculus Examples

$\frac{6 \ln (x) \cdot 1}{7} \cdot \ln (y)$

Step 1

Simplify the numerator.

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Step 1.1

Simplify $6 \ln (x)$ by moving $6$ inside the logarithm.

$\frac{\ln (x^{6}) \cdot 1}{7} \cdot \ln (y)$

Step 1.2

Multiply $\ln (x^{6})$ by $1$ .

$\frac{\ln (x^{6})}{7} \cdot \ln (y)$

Step 2

Rewrite $\frac{\ln (x^{6})}{7}$ as $\frac{1}{7} \ln (x^{6})$ .

$\frac{1}{7} \ln (x^{6}) \cdot \ln (y)$

Step 3

Simplify $\frac{1}{7} \ln (x^{6})$ by moving $\frac{1}{7}$ inside the logarithm.

$\ln ({(x^{6})}^{\frac{1}{7}}) \cdot \ln (y)$

Step 4

Multiply the exponents in ${(x^{6})}^{\frac{1}{7}}$ .

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Step 4.1

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

$\ln (x^{6 (\frac{1}{7})}) \cdot \ln (y)$

Step 4.2

Combine $6$ and $\frac{1}{7}$ .

$\ln (x^{\frac{6}{7}}) \cdot \ln (y)$

$\ln (x^{\frac{6}{7}}) \ln (y)$