Solve 6^m=1

$$6 ^ { m } = 1$$

Solve for m

$$m=0$$

Steps Using Definition of Logarithm

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

$$6^{m}=1$$

Take the logarithm of both sides of the equation.

$$\log(6^{m})=\log(1)$$

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

$$m\log(6)=\log(1)$$

Divide both sides by \log(6).

$$m=\frac{\log(1)}{\log(6)}$$

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

$$m=\log_{6}\left(1\right)$$

Solve for m (complex solution)

$$m=\frac{2\pi n_{1}i}{\ln(6)}$$

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