Solve 6^-a=1

$$6 ^ { - a } = 1$$

Solve for a

$$a=0$$

Steps Using Definition of Logarithm

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

$$6^{-a}=1$$

Take the logarithm of both sides of the equation.

$$\log(6^{-a})=\log(1)$$

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

$$-a\log(6)=\log(1)$$

Divide both sides by \log(6).

$$-a=\frac{\log(1)}{\log(6)}$$

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

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

Divide both sides by -1.

$$a=\frac{0}{-1}$$

Solve for a (complex solution)

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

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