Solve for x f(-2)=3^x

$f (- 2) = 3^{x}$

Step 1

Rewrite the equation as $3^{x} = f (- 2)$ .

$3^{x} = f (- 2)$

Step 2

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

$\ln (3^{x}) = \ln (f (- 2))$

Step 3

Expand $\ln (3^{x})$ by moving $x$ outside the logarithm.

$x \ln (3) = \ln (f (- 2))$

Step 4

Simplify the right side.

Move $- 2$ to the left of $f$ .

$x \ln (3) = \ln (- 2 f)$

Step 5

Divide each term in $x \ln (3) = \ln (- 2 f)$ by $\ln (3)$ and simplify.

Divide each term in $x \ln (3) = \ln (- 2 f)$ by $\ln (3)$ .

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (- 2 f)}{\ln (3)}$

Simplify the left side.

Cancel the common factor of $\ln (3)$ .

Cancel the common factor.

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (- 2 f)}{\ln (3)}$

Divide $x$ by $1$ .

$x = \frac{\ln (- 2 f)}{\ln (3)}$