Solve -486=-6^x-1

$$- 486 = - 6 ^ { x - 1 }$$

Solve for x

$$x=2\log_{6}\left(54\right)\approx 4.452588771$$

Steps Using Definition of Logarithm

Swap sides so that all variable terms are on the left hand side.

$$-6^{x-1}=-486$$

Divide both sides by -1.

$$6^{x-1}=\frac{-486}{-1}$$

Fraction \frac{-486}{-1} can be simplified to 486 by removing the negative sign from both the numerator and the denominator.

$$6^{x-1}=486$$

Take the logarithm of both sides of the equation.

$$\log(6^{x-1})=\log(486)$$

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

$$\left(x-1\right)\log(6)=\log(486)$$

Divide both sides by \log(6).

$$x-1=\frac{\log(486)}{\log(6)}$$

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

$$x-1=\log_{6}\left(486\right)$$

Add 1 to both sides of the equation.

$$x=\log_{6}\left(486\right)-\left(-1\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(6)}+2\log_{6}\left(54\right)$$

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