Solve 16^3n=17

$$16 ^ { 3 n } = 17$$

Solve for n

$$n=\frac{\log_{2}\left(17\right)}{12}\approx 0.340621903$$

Steps Using Definition of Logarithm

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

$$16^{3n}=17$$

Take the logarithm of both sides of the equation.

$$\log(16^{3n})=\log(17)$$

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

$$3n\log(16)=\log(17)$$

Divide both sides by \log(16).

$$3n=\frac{\log(17)}{\log(16)}$$

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

$$3n=\log_{16}\left(17\right)$$

Divide both sides by 3.

$$n=\frac{\log_{2}\left(17\right)}{3\times 4}$$