Solve 2^x+2+2*4=160

$${ 2 }^{ x+2 } +2 \times 4 = 160$$

Solve for x

$$x=\log_{2}\left(19\right)+1\approx 5.247927513$$

Steps Using Definition of Logarithm

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

$$2^{x+2}+8=160$$

Subtract 8 from both sides of the equation.

$$2^{x+2}=152$$

Take the logarithm of both sides of the equation.

$$\log(2^{x+2})=\log(152)$$

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

$$\left(x+2\right)\log(2)=\log(152)$$

Divide both sides by \log(2).

$$x+2=\frac{\log(152)}{\log(2)}$$

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

$$x+2=\log_{2}\left(152\right)$$

Subtract 2 from both sides of the equation.

$$x=\log_{2}\left(152\right)-2$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+\log_{2}\left(38\right)$$

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