Solve 10^x+2+1=3

$${ 10 }^{ x+2 } +1=3$$

Solve for x

$$x=-\log_{10}\left(50\right)\approx -1.698970004$$

Steps Using Definition of Logarithm

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

$$10^{x+2}+1=3$$

Subtract 1 from both sides of the equation.

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

Take the logarithm of both sides of the equation.

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

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

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

Subtract 2 from both sides of the equation.

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

Solve for x (complex solution)

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

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