Precalculus Examples

$\frac{\log (7^{29})}{3}$

Step 1

Rewrite $\frac{\log (7^{29})}{3}$ as $\frac{1}{3} \log (7^{29})$ .

$\frac{1}{3} \log (7^{29})$

Step 2

Simplify $\frac{1}{3} \log (7^{29})$ by moving $\frac{1}{3}$ inside the logarithm.

$\log ({(7^{29})}^{\frac{1}{3}})$

Step 3

Multiply the exponents in ${(7^{29})}^{\frac{1}{3}}$ .

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Step 3.1

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

$\log (7^{29 (\frac{1}{3})})$

Step 3.2

Combine $29$ and $\frac{1}{3}$ .

$\log (7^{\frac{29}{3}})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (7^{\frac{29}{3}})$

Decimal Form:

$8.16928105 \dots$