If 25x−1 = 52x−1 – 100, then the va...
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If 25^{x-1} = 5^{2x-1} – 100, then the value of x is

11th - 12th Class
Maths
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If 25x−1 = 52x−1 – 100, then the value of x is
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( 25^{x-1}=5^{2 x-1}-100 )
( =frac{25^{x}}{25}=frac{5^{2 x}-100}{5} )
( Rightarrow 5^{2 x}=5 cdot 5^{2 x}-2500 )
( Rightarrow 4 cdot 5^{2 x}=2500 )
( Rightarrow 5^{2 x}=625=5^{4} )
( 2 x=4 quad Rightarrow quad  x=2 )

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