Question

# 2⋅5^x+3=6250

$$\displaystyle{2}⋅{5}^{{x}}+{3}={6250}$$

Divide both sides by 2: $$\displaystyle{5}^{{x}}+{3}={3125}$$
Write the right side using base $$\displaystyle{5}.{3125}={5}^{{5}}$$ so: $$\displaystyle{5}{x}+{3}={5}^{{5}}$$
Equate exponents: $$x+3=5$$
Subtract 3 from both sides: $$x=2$$