Solve 2^n=25b

$$2 ^ { n } = 25 b$$

Solve for b

$$b=\frac{2^{n}}{25}$$

Steps for Solving Linear Equation

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

$$25b=2^{n}$$

Divide both sides by 25.

$$\frac{25b}{25}=\frac{2^{n}}{25}$$

Dividing by 25 undoes the multiplication by 25.

$$b=\frac{2^{n}}{25}$$

Solve for n (complex solution)

$$n=\frac{\ln(b)+2\ln(5)}{\ln(2)}+\frac{2\pi n_{1}i}{\ln(2)}$$

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

$$b\neq 0$$

Solve for n

$$n=\frac{\ln(b)+2\ln(5)}{\ln(2)}$$

$$b>0$$