Question

${5}^{2x - 1} - {25}^{x - 1} = 2500 \: \\ find \: x$

Answer 1

5^(2x - 1) - (25)^(x - 1 ) = 2500

5^(2x -1) - (5^2)^(x - 1 ) = 2500

5^(2x - 1 ) - 5^(2x - 2 ) = 2500

5^(2x). 5^(-1) - 5^(2x) .5^(-2)=2500

5^2x ( 1 /5 - 1 / 25 )=2500

5^2x (5 - 1 ) /25 = 2500

5^2x ( 4 /25) = 2500

5^2x = 62500/4

5^2x = 15625

5^2x = (125)^2

5^2x = (5^3)^2

5^2x = 5^6

2x = 6

x = 3

therefore , value of x = 3
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Your Answer : x = 3
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