Solve 9^a=25

$$9 ^ { a } = 25$$

Solve for a

$$a=\log_{3}\left(5\right)\approx 1.464973521$$

Steps Using Definition of Logarithm

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

$$9^{a}=25$$

Take the logarithm of both sides of the equation.

$$\log(9^{a})=\log(25)$$

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

$$a\log(9)=\log(25)$$

Divide both sides by \log(9).

$$a=\frac{\log(25)}{\log(9)}$$

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

$$a=\log_{9}\left(25\right)$$

Solve for a (complex solution)

$$a=\frac{\pi n_{1}i}{\ln(3)}+\log_{3}\left(5\right)$$

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