Evaluate log base 5 of 5(5)^(1/3)

$\log_{5} (5 {(5)}^{\frac{1}{3}})$

Multiply $5$ by ${(5)}^{\frac{1}{3}}$ by adding the exponents.

Multiply $5$ by ${(5)}^{\frac{1}{3}}$ .

Raise $5$ to the power of $1$ .

$\log_{5} (5^{1} {(5)}^{\frac{1}{3}})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\log_{5} (5^{1 + \frac{1}{3}})$

Write $1$ as a fraction with a common denominator.

$\log_{5} (5^{\frac{3}{3} + \frac{1}{3}})$

Combine the numerators over the common denominator.

$\log_{5} (5^{\frac{3 + 1}{3}})$

Add $3$ and $1$ .

$\log_{5} (5^{\frac{4}{3}})$

Use logarithm rules to move $\frac{4}{3}$ out of the exponent.

$\frac{4}{3} \log_{5} (5)$

Logarithm base $5$ of $5$ is $1$ .

$\frac{4}{3} \cdot 1$

Multiply $\frac{4}{3}$ by $1$ .

$\frac{4}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$