Solve for x 5(2^(3x))=8

$5 (2^{3 x}) = 8$

Step 1

Divide each term in $(5 \cdot 2^{3 x}) = 8$ by $5$ and simplify.

Divide each term in $(5 \cdot 2^{3 x}) = 8$ by $5$ .

$\frac{(5 \cdot 2^{3 x})}{5} = \frac{8}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 \cdot 2^{3 x}}{5} = \frac{8}{5}$

Divide $2^{3 x}$ by $1$ .

$2^{3 x} = \frac{8}{5}$

Step 2

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

$\ln (2^{3 x}) = \ln (\frac{8}{5})$

Step 3

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

$3 x \ln (2) = \ln (\frac{8}{5})$

Step 4

Divide each term in $3 x \ln (2) = \ln (\frac{8}{5})$ by $3 \ln (2)$ and simplify.

Divide each term in $3 x \ln (2) = \ln (\frac{8}{5})$ by $3 \ln (2)$ .

$\frac{3 x \ln (2)}{3 \ln (2)} = \frac{\ln (\frac{8}{5})}{3 \ln (2)}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x \ln (2)}{3 \ln (2)} = \frac{\ln (\frac{8}{5})}{3 \ln (2)}$

Rewrite the expression.

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (\frac{8}{5})}{3 \ln (2)}$

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

Cancel the common factor.

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (\frac{8}{5})}{3 \ln (2)}$

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{8}{5})}{3 \ln (2)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (\frac{8}{5})}{3 \ln (2)}$

Decimal Form:

$x = 0.22602396 \dots$