Solve [108/100]^x=7290/6250

$$[ \frac { 108 } { 100 } ] ^ { x } = \frac { 7290 } { 6250 }$$

Solve for x

$$x=2$$

Steps Using Definition of Logarithm

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

$$\left(\frac{27}{25}\right)^{x}=\frac{729}{625}$$

Take the logarithm of both sides of the equation.

$$\log(\left(\frac{27}{25}\right)^{x})=\log(\frac{729}{625})$$

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

$$x\log(\frac{27}{25})=\log(\frac{729}{625})$$

Divide both sides by \log(\frac{27}{25}).

$$x=\frac{\log(\frac{729}{625})}{\log(\frac{27}{25})}$$

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

$$x=\log_{\frac{27}{25}}\left(\frac{729}{625}\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{27}{25})}+2$$

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