Solve 17^3n-3.9=1

$$17 ^ { 3 n - 3.9 } = 1$$

Solve for n

$$n=1.3$$

Steps Using Definition of Logarithm

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

$$17^{3n-3.9}=1$$

Take the logarithm of both sides of the equation.

$$\log(17^{3n-3.9})=\log(1)$$

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

$$\left(3n-3.9\right)\log(17)=\log(1)$$

Divide both sides by \log(17).

$$3n-3.9=\frac{\log(1)}{\log(17)}$$

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

$$3n-3.9=\log_{17}\left(1\right)$$

Add 3.9 to both sides of the equation.

$$3n=-\left(-3.9\right)$$

Divide both sides by 3.

$$n=\frac{3.9}{3}$$