Solve 16^x-2=1/32

$${ 16 }^{ x-2 } = \frac{ 1 }{ 32 }$$

Solve for x

$$x=\frac{3}{4}=0.75$$

Steps Using Definition of Logarithm

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

$$16^{x-2}=\frac{1}{32}$$

Take the logarithm of both sides of the equation.

$$\log(16^{x-2})=\log(\frac{1}{32})$$

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

$$\left(x-2\right)\log(16)=\log(\frac{1}{32})$$

Divide both sides by \log(16).

$$x-2=\frac{\log(\frac{1}{32})}{\log(16)}$$

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

$$x-2=\log_{16}\left(\frac{1}{32}\right)$$

Add 2 to both sides of the equation.

$$x=-\frac{5}{4}-\left(-2\right)$$

Solve for x (complex solution)

$$x=\frac{i\pi n_{1}}{2\ln(2)}+\frac{3}{4}$$

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