Precalculus Examples

$4^{\log_{49} (100)}$

Step 1

Rewrite $\log_{49} (100)$ using the change of base formula.

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Step 1.1

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 $0$ .

$4^{\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}}$

Step 1.2

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

$4^{\frac{\log (100)}{\log (49)}}$

Step 2

Logarithm base $10$ of $100$ is $2$ .

$4^{\frac{2}{\log (49)}}$

Step 3

Rewrite $\log (49)$ as $\log (7^{2})$ .

$4^{\frac{2}{\log (7^{2})}}$

Step 4

Expand $\log (7^{2})$ by moving $2$ outside the logarithm.

$4^{\frac{2}{2 \log (7)}}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Cancel the common factor.

$4^{\frac{2}{2 \log (7)}}$

Step 5.2

Rewrite the expression.

$4^{\frac{1}{\log (7)}}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$4^{\frac{1}{\log (7)}}$

Decimal Form:

$5.15720475 \dots$