Evaluate Using the Given Value 7^(2x)=117 , 649

$7^{2 x} = 117$ , $649$

Step 1

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

$\ln (7^{2 x}) = \ln (117)$

Step 2

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

$2 x \ln (7) = \ln (117)$

Step 3

Divide each term in $2 x \ln (7) = \ln (117)$ by $2 \ln (7)$ and simplify.

Divide each term in $2 x \ln (7) = \ln (117)$ by $2 \ln (7)$ .

$\frac{2 x \ln (7)}{2 \ln (7)} = \frac{\ln (117)}{2 \ln (7)}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x \ln (7)}{2 \ln (7)} = \frac{\ln (117)}{2 \ln (7)}$

Rewrite the expression.

$\frac{x \ln (7)}{\ln (7)} = \frac{\ln (117)}{2 \ln (7)}$

Cancel the common factor of $\ln (7)$ .

Cancel the common factor.

$\frac{x \ln (7)}{\ln (7)} = \frac{\ln (117)}{2 \ln (7)}$

Divide $x$ by $1$ .

$x = \frac{\ln (117)}{2 \ln (7)}$

Step 4

Replace the variable $x$ with $\frac{\ln (117)}{2 \ln (7)}$ in the expression.

$649$