Solve 1*9=(1+0.09)^n

$$1 \cdot 9 = ( 1 + 0.09 ) ^ { n }$$

Solve for n

$$n=2\log_{1.09}\left(3\right)\approx 25.496441344$$

Steps Using Definition of Logarithm

Multiply 1 and 9 to get 9.

$$9=\left(1+0.09\right)^{n}$$

Add 1 and 0.09 to get 1.09.

$$9=1.09^{n}$$

Swap sides so that all variable terms are on the left hand side.

$$1.09^{n}=9$$

Take the logarithm of both sides of the equation.

$$\log(1.09^{n})=\log(9)$$

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

$$n\log(1.09)=\log(9)$$

Divide both sides by \log(1.09).

$$n=\frac{\log(9)}{\log(1.09)}$$

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

$$n=\log_{1.09}\left(9\right)$$