Solve 3.714^x+1=50s

$$3.714 ^ { x + 1 } = 50 s$$

Solve for s

$$s=\frac{1857\times 3.714^{x}}{25000}$$

Steps for Solving Linear Equation

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

$$50s=3.714^{x+1}$$

Divide both sides by 50.

$$\frac{50s}{50}=\frac{3.714^{x+1}}{50}$$

Dividing by 50 undoes the multiplication by 50.

$$s=\frac{3.714^{x+1}}{50}$$

Divide 3.714^{1+x} by 50.

$$s=\frac{1857\times 3.714^{x}}{25000}$$

Solve for x (complex solution)

$$x=\frac{\ln(s)-\ln(0.07428)}{\ln(3.714)}+\frac{i\times 2\pi n_{1}}{\ln(3.714)}$$

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

$$s\neq 0$$

Solve for x

$$x=-\frac{-\ln(s)+\ln(0.07428)}{\ln(3.714)}$$

$$s>0$$