Solve for x 324^x=2/3

$324^{x} = \frac{2}{3}$

Step 1

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

$\ln (324^{x}) = \ln (\frac{2}{3})$

Step 2

Expand $\ln (324^{x})$ by moving $x$ outside the logarithm.

$x \ln (324) = \ln (\frac{2}{3})$

Step 3

Divide each term in $x \ln (324) = \ln (\frac{2}{3})$ by $\ln (324)$ and simplify.

Divide each term in $x \ln (324) = \ln (\frac{2}{3})$ by $\ln (324)$ .

$\frac{x \ln (324)}{\ln (324)} = \frac{\ln (\frac{2}{3})}{\ln (324)}$

Simplify the left side.

Cancel the common factor of $\ln (324)$ .

Cancel the common factor.

$\frac{x \ln (324)}{\ln (324)} = \frac{\ln (\frac{2}{3})}{\ln (324)}$

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{2}{3})}{\ln (324)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (\frac{2}{3})}{\ln (324)}$

Decimal Form:

$x = - 0.07014065 \dots$