Solve 3^x+2=3^5

$$3 ^ { x + 2 } = 3 ^ { 5 }$$

Solve for x

$$x=3$$

Steps Using Definition of Logarithm

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

$$3^{x+2}=243$$

Take the logarithm of both sides of the equation.

$$\log(3^{x+2})=\log(243)$$

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

$$\left(x+2\right)\log(3)=\log(243)$$

Divide both sides by \log(3).

$$x+2=\frac{\log(243)}{\log(3)}$$

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

$$x+2=\log_{3}\left(243\right)$$

Subtract 2 from both sides of the equation.

$$x=5-2$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(3)}+3$$

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