Solve 9^x=243

$$9 ^ { x } = 243$$

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps Using Definition of Logarithm

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

$$9^{x}=243$$

Take the logarithm of both sides of the equation.

$$\log(9^{x})=\log(243)$$

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

$$x\log(9)=\log(243)$$

Divide both sides by \log(9).

$$x=\frac{\log(243)}{\log(9)}$$

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

$$x=\log_{9}\left(243\right)$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(3)}+\frac{5}{2}$$

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