Solve (11/10)^n=(11/10)^3

$$( \frac { 11 } { 10 } ) ^ { n } = ( \frac { 11 } { 10 } ) ^ { 3 }$$

Solve for n

$$n=3$$

Steps Using Definition of Logarithm

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

$$\left(\frac{11}{10}\right)^{n}=\frac{1331}{1000}$$

Take the logarithm of both sides of the equation.

$$\log(\left(\frac{11}{10}\right)^{n})=\log(\frac{1331}{1000})$$

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

$$n\log(\frac{11}{10})=\log(\frac{1331}{1000})$$

Divide both sides by \log(\frac{11}{10}).

$$n=\frac{\log(\frac{1331}{1000})}{\log(\frac{11}{10})}$$

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

$$n=\log_{\frac{11}{10}}\left(\frac{1331}{1000}\right)$$