Find $x$: $5^{x+2} - 5^{x+1} = 500$.
Find $x$: $5^{x+2} - 5^{x+1} = 500$.
- $1$
- $2$
- $3$
- $0$
Solution
Factor: $5^{x+1}(5 - 1) = 500 \Rightarrow 4 \cdot 5^{x+1} = 500 \Rightarrow 5^{x+1} = 125 = 5^{3} \Rightarrow x + 1 = 3 \Rightarrow x = 2$.
Asked in: IMO
Practice more EXPONENTS AND POWERS questions on Aicharya