Solve 16^x+1=4

$$16 ^ { x + 1 } = 4$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps Using Definition of Logarithm

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

$$16^{x+1}=4$$

Take the logarithm of both sides of the equation.

$$\log(16^{x+1})=\log(4)$$

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

$$\left(x+1\right)\log(16)=\log(4)$$

Divide both sides by \log(16).

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

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

$$x+1=\log_{16}\left(4\right)$$

Subtract 1 from both sides of the equation.

$$x=\frac{1}{2}-1$$

Solve for x (complex solution)

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

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