Finite Math Examples

$6^{5 x} = 92$ , $184$

Step 1

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

$\ln (6^{5 x}) = \ln (92)$

Step 2

Expand $\ln (6^{5 x})$ by moving $5 x$ outside the logarithm.

$5 x \ln (6) = \ln (92)$

Step 3

Divide each term in $5 x \ln (6) = \ln (92)$ by $5 \ln (6)$ and simplify.

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Step 3.1

Divide each term in $5 x \ln (6) = \ln (92)$ by $5 \ln (6)$ .

$\frac{5 x \ln (6)}{5 \ln (6)} = \frac{\ln (92)}{5 \ln (6)}$

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.

$\frac{5 x \ln (6)}{5 \ln (6)} = \frac{\ln (92)}{5 \ln (6)}$

Step 3.2.1.2

Rewrite the expression.

$\frac{x \ln (6)}{\ln (6)} = \frac{\ln (92)}{5 \ln (6)}$

Step 3.2.2

Cancel the common factor of $\ln (6)$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{x \ln (6)}{\ln (6)} = \frac{\ln (92)}{5 \ln (6)}$

Step 3.2.2.2

Divide $x$ by $1$ .

$x = \frac{\ln (92)}{5 \ln (6)}$

Step 4

Replace the variable $x$ with $\frac{\ln (92)}{5 \ln (6)}$ in the expression.

$184$