Evaluate 5^(3- log base 5 of 7)

$5^{3 - \log_{5} (7)}$

Step 1

The change of base rule can be used if $a$ and $b$ are greater than $0$ and not equal to $1$ , and $x$ is greater than $0$ .

$5^{3 - \log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}}$

Step 2

Substitute in values for the variables in the change of base formula, using $b = 10$ .

$5^{3 - \frac{\log (7)}{\log (5)}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$5^{3 - \frac{\log (7)}{\log (5)}}$

Decimal Form:

$17.85714285 \dots$