Solve 10^x+2-12=22

$${ 10 }^{ x+2 } -12=22$$

Solve for x

$$x=-\log_{10}\left(\frac{50}{17}\right)\approx -0.468521083$$

Steps Using Definition of Logarithm

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

$$10^{x+2}-12=22$$

Add 12 to both sides of the equation.

$$10^{x+2}=34$$

Take the logarithm of both sides of the equation.

$$\log(10^{x+2})=\log(34)$$

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

$$\left(x+2\right)\log(10)=\log(34)$$

Subtract 2 from both sides of the equation.

$$x=\log(34)-2$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(10)}-\log_{10}\left(\frac{50}{17}\right)$$

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