Question

Solve
$({ \sqrt{5} })^{4x - 4} - {5}^{2x - 3} = 20$

Answer 1

Heya !! ☺

(√5)^4x-4 - (5)^2x-3 = 20

=> (5)^1/2(4x-4) - (5)^2x-3 = 20

=> (5)^(2x-2) - (5)^(2x-3) = 20

=> 5^(2x) × 5^(-2) - 5^(2x) × 5^(-3)

=> 5^(2x) [5^(-2) - 5^(-3)]

=> 5^(2x) [ 1/5^2 - 1/5^3 ]

=> 5^(2x) [(5-1)/5^3]

=> 5^(2x) [4/5^3]

=> 5^(2x-3) = 20/4

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

=> 5^(2x-3) = 5^(1)

=> 2x - 3 = 1

=> 2x = 3 + 1

=> 2x = 4

=> x = 4/2

=> x = 2

Hope my ans.'s satisfactory.

Answer 2

Hey

[ ( √5 ) ^ 4x - 4 ] - [ ( 5 ) ^ 2x - 3 ] = 20

=> [ ( √5 ) ^ 4x - 4 ] - [ (√5 ² ) ^ 2x - 3 ] = 20

=> [ ( √5 ) ^ 4x - 4 ] - [ ( √5 ) ^ 4x - 6 ] = 20

=> (√5 ) ^ 4x . ( √5 ) ^4 - ( √5 ) ^4x . ( √5 ) ^ 6 = 20

=> ( √5 ) ^4x [ (√5 ) ^( -4 ) - ( √5 ) ^ ( - 6) ] = 20

=> ( √ 5² ) ^ 2x [ ( 5 ) ^ ( -2 ) - ( 5 ) ^ ( - 3 ) ] = 20

=> 5^ 2x [ 1 / 5² - 1 / 5³ ] = 20

=> 5 ^ 2x [ 5 - 1 / 5³ ] = 20

=> 5 ^ 2x [ 4 / 5³ ] = 20

=> 5^ 2x = 20 * 125 / 4

=> 5 ^ 2x = 625

=> 5 ^ 2x = 5⁴

=> 2x = 4

=> x = 2

thanks :)

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