Solve for x 4+3^(5x)=8

$4 + 3^{5 x} = 8$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$3^{5 x} = 8 - 4$

Subtract $4$ from $8$ .

$3^{5 x} = 4$

Step 2

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

$\ln (3^{5 x}) = \ln (4)$

Step 3

Expand $\ln (3^{5 x})$ by moving $5 x$ outside the logarithm.

$5 x \ln (3) = \ln (4)$

Step 4

Divide each term in $5 x \ln (3) = \ln (4)$ by $5 \ln (3)$ and simplify.

Divide each term in $5 x \ln (3) = \ln (4)$ by $5 \ln (3)$ .

$\frac{5 x \ln (3)}{5 \ln (3)} = \frac{\ln (4)}{5 \ln (3)}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x \ln (3)}{5 \ln (3)} = \frac{\ln (4)}{5 \ln (3)}$

Rewrite the expression.

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (4)}{5 \ln (3)}$

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

Cancel the common factor.

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (4)}{5 \ln (3)}$

Divide $x$ by $1$ .

$x = \frac{\ln (4)}{5 \ln (3)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (4)}{5 \ln (3)}$

Decimal Form:

$x = 0.25237190 \dots$