Solve 15^x=9

$${ 15 }^{ x } =9$$

Solve for x

$$x=2\log_{15}\left(3\right)\approx 0.811367742$$

Steps Using Definition of Logarithm

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

$$15^{x}=9$$

Take the logarithm of both sides of the equation.

$$\log(15^{x})=\log(9)$$

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

$$x\log(15)=\log(9)$$

Divide both sides by \log(15).

$$x=\frac{\log(9)}{\log(15)}$$

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

$$x=\log_{15}\left(9\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(15)}+2\log_{15}\left(3\right)$$

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