Question

Solve for x
$5^{x+1}-5^{x-2}=620$

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

3

$5^{x+1}-5^{x-2}=620$

$\Rightarrow 5^{x}5-5^x{5}^{-2}=620$

$\Rightarrow 5^x(5-\frac{1}{25})=620$

$\Rightarrow 5^x\left(\frac{125-1}{25}\right)=620$

$\Rightarrow 5^x\left(\frac{124}{25}\right)=620$

$\Rightarrow 5^x\left(\frac{124}{5^2}\right)=620$

$\Rightarrow 5^{x-2}=\frac{620}{124}=\frac{155}{31}=5$

$\Rightarrow 5^{x-2}=5$

$\Rightarrow \frac{5^x}{5^2}=5$

$\therefore 5^x=5^1{5}^2=5^{1+2}=5^3$

$\Rightarrow 5^x=5^3$

Since bases are same, we can equate the powers,

$\therefore x=3$