Find All Complex Solutions 2^(3x)=10

$2^{3 x} = 10$

Step 1

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

$\ln (2^{3 x}) = \ln (10)$

Step 2

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

$3 x \ln (2) = \ln (10)$

Step 3

Divide each term in $3 x \ln (2) = \ln (10)$ by $3 \ln (2)$ and simplify.

Divide each term in $3 x \ln (2) = \ln (10)$ by $3 \ln (2)$ .

$\frac{3 x \ln (2)}{3 \ln (2)} = \frac{\ln (10)}{3 \ln (2)}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x \ln (2)}{3 \ln (2)} = \frac{\ln (10)}{3 \ln (2)}$

Rewrite the expression.

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (10)}{3 \ln (2)}$

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

Cancel the common factor.

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (10)}{3 \ln (2)}$

Divide $x$ by $1$ .

$x = \frac{\ln (10)}{3 \ln (2)}$