Question

Find x.

5^x + 5^{x – 1} = 750

Answer 1

We have, 5^x + 5^{x – 1} = 750

⇒ ${\displaystyle 5^x+\frac{5^x}{5}=750}$  ...${\displaystyle [\because a^{-m}=\frac{1}{a^m}]}$

⇒ ${\displaystyle 5^x(1+\frac{1}{5})=750}$

⇒ ${\displaystyle 5^x\left(\frac{6}{5}\right)=750}$

⇒ ${\displaystyle 5^x=750\times \frac{5}{6}}$

⇒ 5^x = 125 × 5

⇒ 5^x = 625

⇒ 5^x = 5⁴

On comparing the power of 5, we get

x = 4