Solve (105/100)^x=9261/8000

$$( \frac { 105 } { 100 } ) ^ { x } = \frac { 9261 } { 8000 }$$

Solve for x

$$x=3$$

Steps Using Definition of Logarithm

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

$$\left(\frac{21}{20}\right)^{x}=\frac{9261}{8000}$$

Take the logarithm of both sides of the equation.

$$\log(\left(\frac{21}{20}\right)^{x})=\log(\frac{9261}{8000})$$

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

$$x\log(\frac{21}{20})=\log(\frac{9261}{8000})$$

Divide both sides by \log(\frac{21}{20}).

$$x=\frac{\log(\frac{9261}{8000})}{\log(\frac{21}{20})}$$

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

$$x=\log_{\frac{21}{20}}\left(\frac{9261}{8000}\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{21}{20})}+\log_{\frac{21}{20}}\left(\frac{9261}{8000}\right)$$

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