Solve (108/100)^x=729y/6259

$$( \frac { 108 } { 100 } ) ^ { x } = \frac { 729 y } { 6259 }$$

Solve for y

$$y=\frac{6259\times \left(\frac{27}{25}\right)^{x}}{729}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6259.

$$6259\times \left(\frac{108}{100}\right)^{x}=729y$$

Reduce the fraction \frac{108}{100} to lowest terms by extracting and canceling out 4.

$$6259\times \left(\frac{27}{25}\right)^{x}=729y$$

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

$$729y=6259\times \left(\frac{27}{25}\right)^{x}$$

Divide both sides by 729.

$$\frac{729y}{729}=\frac{6259\times \left(\frac{27}{25}\right)^{x}}{729}$$

Dividing by 729 undoes the multiplication by 729.

$$y=\frac{6259\times \left(\frac{27}{25}\right)^{x}}{729}$$

Solve for x (complex solution)

$$x=\frac{\ln(y)+\ln(\frac{729}{6259})}{\ln(\frac{27}{25})}+\frac{2\pi n_{1}i}{\ln(\frac{27}{25})}$$

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

$$y\neq 0$$

Solve for x

$$x=\frac{\ln(y)+\ln(\frac{729}{6259})}{\ln(\frac{27}{25})}$$

$$y>0$$