Solve 9^x+1=36

$$9 ^ { x + 1 } = 36$$

Solve for x

$$x=\log_{3}\left(6\right)-1\approx 0.630929754$$

Steps Using Definition of Logarithm

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

$$9^{x+1}=36$$

Take the logarithm of both sides of the equation.

$$\log(9^{x+1})=\log(36)$$

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

$$\left(x+1\right)\log(9)=\log(36)$$

Divide both sides by \log(9).

$$x+1=\frac{\log(36)}{\log(9)}$$

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

$$x+1=\log_{9}\left(36\right)$$

Subtract 1 from both sides of the equation.

$$x=\log_{3}\left(6\right)-1$$

Solve for x (complex solution)

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

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