Precalculus Examples

$\frac{\log (8) \cdot 7}{9} z$

Step 1

Rewrite $\log (8)$ as $\log (2^{3})$ .

$\frac{\log (2^{3}) \cdot 7}{9} z$

Step 2

Expand $\log (2^{3})$ by moving $3$ outside the logarithm.

$\frac{3 \log (2) \cdot 7}{9} z$

Step 3

Cancel the common factor of $3$ and $9$ .

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Step 3.1

Factor $3$ out of $3 \log (2) \cdot 7$ .

$\frac{3 (\log (2) \cdot 7)}{9} z$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $9$ .

$\frac{3 (\log (2) \cdot 7)}{3 \cdot 3} z$

Step 3.2.2

Cancel the common factor.

$\frac{3 (\log (2) \cdot 7)}{3 \cdot 3} z$

Step 3.2.3

Rewrite the expression.

$\frac{\log (2) \cdot 7}{3} z$

Step 4

Simplify the numerator.

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Step 4.1

Reorder $\log (2)$ and $7$ .

$\frac{7 \cdot \log (2)}{3} z$

Step 4.2

Simplify $7 \cdot \log (2)$ by moving $7$ inside the logarithm.

$\frac{\log (2^{7})}{3} z$

Step 5

Raise $2$ to the power of $7$ .

$\frac{\log (128)}{3} z$

Step 6

Rewrite $\frac{\log (128)}{3}$ as $\frac{1}{3} \log (128)$ .

$\frac{1}{3} \log (128) z$

Step 7

Simplify $\frac{1}{3} \log (128)$ by moving $\frac{1}{3}$ inside the logarithm.

$\log (128^{\frac{1}{3}}) z$

Step 8

Reorder factors in $\log (128^{\frac{1}{3}}) z$ .

$z \log (128^{\frac{1}{3}})$