Solve 6^3m+2=1

$$6 ^ { 3 m + 2 } = 1$$

Solve for m

$$m=-\frac{2}{3}\approx -0.666666667$$

Steps Using Definition of Logarithm

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

$$6^{3m+2}=1$$

Take the logarithm of both sides of the equation.

$$\log(6^{3m+2})=\log(1)$$

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

$$\left(3m+2\right)\log(6)=\log(1)$$

Divide both sides by \log(6).

$$3m+2=\frac{\log(1)}{\log(6)}$$

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

$$3m+2=\log_{6}\left(1\right)$$

Subtract 2 from both sides of the equation.

$$3m=-2$$

Divide both sides by 3.

$$m=-\frac{2}{3}$$

Solve for m (complex solution)

$$m=\frac{i\times 2\pi n_{1}}{3\ln(6)}-\frac{2}{3}$$

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