Solve (1.10)^n=1/.3855

$$( 1.10 ) ^ { n } = \frac { 1 } { .3855 }$$

Solve for n

$$n=\log_{1.1}\left(\frac{2000}{771}\right)\approx 10.001178132$$

Steps Using Definition of Logarithm

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

$$1.1^{n}=\frac{2000}{771}$$

Take the logarithm of both sides of the equation.

$$\log(1.1^{n})=\log(\frac{2000}{771})$$

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

$$n\log(1.1)=\log(\frac{2000}{771})$$

Divide both sides by \log(1.1).

$$n=\frac{\log(\frac{2000}{771})}{\log(1.1)}$$

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

$$n=\log_{1.1}\left(\frac{2000}{771}\right)$$