Solve for x 8+5^x=1008

$8 + 5^{x} = 1008$

Step 1

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

Subtract $8$ from both sides of the equation.

$5^{x} = 1008 - 8$

Subtract $8$ from $1008$ .

$5^{x} = 1000$

Step 2

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

$\ln (5^{x}) = \ln (1000)$

Step 3

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

$x \ln (5) = \ln (1000)$

Step 4

Divide each term in $x \ln (5) = \ln (1000)$ by $\ln (5)$ and simplify.

Divide each term in $x \ln (5) = \ln (1000)$ by $\ln (5)$ .

$\frac{x \ln (5)}{\ln (5)} = \frac{\ln (1000)}{\ln (5)}$

Simplify the left side.

Cancel the common factor of $\ln (5)$ .

Cancel the common factor.

$\frac{x \ln (5)}{\ln (5)} = \frac{\ln (1000)}{\ln (5)}$

Divide $x$ by $1$ .

$x = \frac{\ln (1000)}{\ln (5)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (1000)}{\ln (5)}$

Decimal Form:

$x = 4.29202967 \dots$