Solve 8^y-2=16

$$8 ^ { y - 2 } = 16$$

Solve for y

$$y = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

Steps Using Definition of Logarithm

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

$$8^{y-2}=16$$

Take the logarithm of both sides of the equation.

$$\log(8^{y-2})=\log(16)$$

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

$$\left(y-2\right)\log(8)=\log(16)$$

Divide both sides by \log(8).

$$y-2=\frac{\log(16)}{\log(8)}$$

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

$$y-2=\log_{8}\left(16\right)$$

Add 2 to both sides of the equation.

$$y=\frac{4}{3}-\left(-2\right)$$

Solve for y (complex solution)

$$y=\frac{i\times 2\pi n_{1}}{3\ln(2)}+\frac{10}{3}$$

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