Question

# If 25^{x-1} = 5^{2x-1} – 100, then the value of x is

Solution

( 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 )