Solve 20^8v=35.5

$$20 ^ { 8 v } = 35.5$$

Solve for v

$$v=\frac{\log_{20}\left(35.5\right)}{8}\approx 0.148942411$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$20^{8v}=35.5$$

Take the logarithm of both sides of the equation.

$$\log(20^{8v})=\log(35.5)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$8v\log(20)=\log(35.5)$$

Divide both sides by \log(20).

$$8v=\frac{\log(35.5)}{\log(20)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$8v=\log_{20}\left(35.5\right)$$

Divide both sides by 8.

$$v=\frac{\ln(\frac{71}{2})}{8\ln(20)}$$