Solve for y 10(8^y)=500

$10 (8^{y}) = 500$

Divide each term in $(10 \cdot 8^{y}) = 500$ by $10$ and simplify.

Divide each term in $(10 \cdot 8^{y}) = 500$ by $10$ .

$\frac{(10 \cdot 8^{y})}{10} = \frac{500}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 \cdot 8^{y}}{10} = \frac{500}{10}$

Divide $8^{y}$ by $1$ .

$8^{y} = \frac{500}{10}$

Simplify the right side.

Divide $500$ by $10$ .

$8^{y} = 50$

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

$\ln (8^{y}) = \ln (50)$

Expand $\ln (8^{y})$ by moving $y$ outside the logarithm.

$y \ln (8) = \ln (50)$

Divide each term in $y \ln (8) = \ln (50)$ by $\ln (8)$ and simplify.

Divide each term in $y \ln (8) = \ln (50)$ by $\ln (8)$ .

$\frac{y \ln (8)}{\ln (8)} = \frac{\ln (50)}{\ln (8)}$

Simplify the left side.

Cancel the common factor of $\ln (8)$ .

Cancel the common factor.

$\frac{y \ln (8)}{\ln (8)} = \frac{\ln (50)}{\ln (8)}$

Divide $y$ by $1$ .

$y = \frac{\ln (50)}{\ln (8)}$

The result can be shown in multiple forms.

Exact Form:

$y = \frac{\ln (50)}{\ln (8)}$

Decimal Form:

$y = 1.88128539 \dots$