Solving a power equation — Number System Aptitude Question
Solving a power equation: If 5ˣ = 3125, what is the value of 5⁽ˣ⁻³⁾? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 40 seconds
Question
If 5ˣ = 3125, what is the value of 5⁽ˣ⁻³⁾?
Options
- 5
- 25
- 125
- 625
Show the answer and the worked solution
Correct answer: B. 25
Worked solution
- 3125 = 5⁵, so x = 5.
- 5⁽ˣ⁻³⁾ = 5² = 25.
Answer: 25.
The idea
Rewrite both sides with the same base and equate the exponents. Worth memorising: 5⁵ = 3125, 2¹⁰ = 1024, 3⁵ = 243, 7⁴ = 2401.
Shortcut. No need to find x: 5⁽ˣ⁻³⁾ = 5ˣ ÷ 5³ = 3125 ÷ 125 = 25.
Common trap. 125 — from taking 3125 as 5⁶ (5⁶ is 15,625), which makes x − 3 = 3.