Solve for x 2^(3x)=91

$2^{3 x} = 91$

Step 1

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

$\ln (2^{3 x}) = \ln (91)$

Step 2

Expand $\ln (2^{3 x})$ by moving $3 x$ outside the logarithm.

$3 x \ln (2) = \ln (91)$

Step 3

Divide each term in $3 x \ln (2) = \ln (91)$ by $3 \ln (2)$ and simplify.

Divide each term in $3 x \ln (2) = \ln (91)$ by $3 \ln (2)$ .

$\frac{3 x \ln (2)}{3 \ln (2)} = \frac{\ln (91)}{3 \ln (2)}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x \ln (2)}{3 \ln (2)} = \frac{\ln (91)}{3 \ln (2)}$

Rewrite the expression.

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (91)}{3 \ln (2)}$

Cancel the common factor of $\ln (2)$ .

Cancel the common factor.

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (91)}{3 \ln (2)}$

Divide $x$ by $1$ .

$x = \frac{\ln (91)}{3 \ln (2)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (91)}{3 \ln (2)}$

Decimal Form:

$x = 2.16926488 \dots$