Algebra Examples

$4^{5 k} = 37$

Step 1

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (4^{5 k}) = \ln (37)$

Step 2

Expand $\ln (4^{5 k})$ by moving $5 k$ outside the logarithm.

$5 k \ln (4) = \ln (37)$

Step 3

Divide each term in $5 k \ln (4) = \ln (37)$ by $5 \ln (4)$ and simplify.

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Step 3.1

Divide each term in $5 k \ln (4) = \ln (37)$ by $5 \ln (4)$ .

$\frac{5 k \ln (4)}{5 \ln (4)} = \frac{\ln (37)}{5 \ln (4)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{5 k \ln (4)}{5 \ln (4)} = \frac{\ln (37)}{5 \ln (4)}$

Step 3.2.1.2

Rewrite the expression.

$\frac{k \ln (4)}{\ln (4)} = \frac{\ln (37)}{5 \ln (4)}$

Step 3.2.2

Cancel the common factor of $\ln (4)$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{k \ln (4)}{\ln (4)} = \frac{\ln (37)}{5 \ln (4)}$

Step 3.2.2.2

Divide $k$ by $1$ .

$k = \frac{\ln (37)}{5 \ln (4)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$k = \frac{\ln (37)}{5 \ln (4)}$

Decimal Form:

$k = 0.52094533 \dots$