Solve f:y=(3/2)^x

$$f : y = ( \frac { 3 } { 2 } ) ^ { x }$$

Solve for f

$$f=y\times \left(\frac{3}{2}\right)^{x}$$

$$y\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{1}{y}f=\left(\frac{3}{2}\right)^{x}$$

Divide both sides by y^{-1}.

$$\frac{\frac{1}{y}fy}{1}=\frac{\left(\frac{3}{2}\right)^{x}y}{1}$$

Dividing by y^{-1} undoes the multiplication by y^{-1}.

$$f=\frac{\left(\frac{3}{2}\right)^{x}y}{1}$$

Divide \left(\frac{3}{2}\right)^{x} by y^{-1}.

$$f=y\times \left(\frac{3}{2}\right)^{x}$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{3}{2})}+\log_{\frac{3}{2}}\left(\frac{f}{y}\right)$$

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

$$f\neq 0\text{ and }y\neq 0$$

Solve for x

$$x=\log_{\frac{3}{2}}\left(\frac{f}{y}\right)$$

$$\left(f<0\text{ and }y<0\right)\text{ or }\left(f>0\text{ and }y>0\right)$$