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

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Solution

The correct option is A 3
$5^{x + 1} - 5^{x - 2} = 620$

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

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

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

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

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

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

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

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

$∴ 5^{x} = 5^{1} 5^{2} = 5^{1 + 2} = 5^{3}$

$\Rightarrow 5^{x} = 5^{3}$

Since bases are same, we can equate the powers,

$∴ x = 3$

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