Solve 17^x=1

$$17 ^ { x } = 1$$

Solve for x

$$x=0$$

Steps Using Definition of Logarithm

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

$$17^{x}=1$$

Take the logarithm of both sides of the equation.

$$\log(17^{x})=\log(1)$$

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

$$x\log(17)=\log(1)$$

Divide both sides by \log(17).

$$x=\frac{\log(1)}{\log(17)}$$

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

$$x=\log_{17}\left(1\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(17)}$$

$$n_{1}\in \mathrm{Z}$$