Solve f1/5^-y=25(5^4-2y)

$$f \frac { 1 } { 5 ^ { - y } } = 25 ( 5 ^ { 4 - 2 y } )$$

Solve for f

$$f=\frac{15625}{5^{3y}}$$

Steps for Solving Linear Equation

Express f\times \frac{1}{5^{-y}} as a single fraction.

$$\frac{f}{5^{-y}}=25\times 5^{4-2y}$$

The equation is in standard form.

$$5^{y}f=25\times 5^{4-2y}$$

Divide both sides by 5^{y}.

$$\frac{5^{y}f}{5^{y}}=\frac{5^{6-2y}}{5^{y}}$$

Dividing by 5^{y} undoes the multiplication by 5^{y}.

$$f=\frac{5^{6-2y}}{5^{y}}$$

Divide 5^{6-2y} by 5^{y}.

$$f=5^{6-3y}$$

Solve for y (complex solution)

$$y=-\frac{\log_{5}\left(f\right)}{3}+\frac{2\pi n_{1}i}{3\ln(5)}+2$$

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

$$f\neq 0$$

Solve for y

$$y=-\frac{\log_{5}\left(f\right)}{3}+2$$

$$f>0$$