Solve 4^x-3=1/16

$$4 ^ { x - 3 } = \frac { 1 } { 16 }$$

Solve for x

$$x=1$$

Steps Using Definition of Logarithm

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

$$4^{x-3}=\frac{1}{16}$$

Take the logarithm of both sides of the equation.

$$\log(4^{x-3})=\log(\frac{1}{16})$$

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

$$\left(x-3\right)\log(4)=\log(\frac{1}{16})$$

Divide both sides by \log(4).

$$x-3=\frac{\log(\frac{1}{16})}{\log(4)}$$

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

$$x-3=\log_{4}\left(\frac{1}{16}\right)$$

Add 3 to both sides of the equation.

$$x=-2-\left(-3\right)$$

Solve for x (complex solution)

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

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