Precalculus Examples

$8 \log_{6} (x) + \frac{3 \log_{6} (y) (- 1)}{2} \cdot \log_{6} (z)$

Step 1

Simplify $8 \log_{6} (x)$ by moving $8$ inside the logarithm.

$\log_{6} (x^{8}) + \frac{3 \log_{6} (y) (- 1)}{2} \cdot \log_{6} (z)$

Step 2

Simplify $3 \log_{6} (y)$ by moving $3$ inside the logarithm.

$\log_{6} (x^{8}) + \frac{\log_{6} (y^{3}) \cdot - 1}{2} \cdot \log_{6} (z)$

Step 3

Rewrite $\frac{\log_{6} (y^{3}) \cdot - 1}{2}$ as $\frac{- 1}{2} \log_{6} (y^{3})$ .

$\log_{6} (x^{8}) + \frac{- 1}{2} \log_{6} (y^{3}) \cdot \log_{6} (z)$

Step 4

Simplify $\frac{- 1}{2} \log_{6} (y^{3})$ by moving $- \frac{- 1}{2}$ inside the logarithm.

$\log_{6} (x^{8}) - \log_{6} ({(y^{3})}^{- \frac{- 1}{2}}) \cdot \log_{6} (z)$

Step 5

Multiply the exponents in ${(y^{3})}^{- \frac{- 1}{2}}$ .

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Step 5.1

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

$\log_{6} (x^{8}) - \log_{6} (y^{3 (- \frac{- 1}{2})}) \cdot \log_{6} (z)$

Step 5.2

Move the negative in front of the fraction.

$\log_{6} (x^{8}) - \log_{6} (y^{3 (- - \frac{1}{2})}) \cdot \log_{6} (z)$

Step 5.3

Multiply $- - \frac{1}{2}$ .

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Step 5.3.1

Multiply $- 1$ by $- 1$ .

$\log_{6} (x^{8}) - \log_{6} (y^{3 (1 (\frac{1}{2}))}) \cdot \log_{6} (z)$

Step 5.3.2

Multiply $\frac{1}{2}$ by $1$ .

$\log_{6} (x^{8}) - \log_{6} (y^{3 (\frac{1}{2})}) \cdot \log_{6} (z)$

Step 5.4

Combine $3$ and $\frac{1}{2}$ .

$\log_{6} (x^{8}) - \log_{6} (y^{\frac{3}{2}}) \cdot \log_{6} (z)$

$\log_{6} (x^{8}) - \log_{6} (y^{\frac{3}{2}}) \log_{6} (z)$