Question

25^x+2 = 5^x-4 *125^x

Answer 1

25^(x+2) = 5^(x-4) × 125^x

(5^2)^(x+2) = 5^(x-4) × (5^3)^x

5^(2x+4) = 5^(x-4) × 5^3x

5^(2x+4) = 5^(x-4+3x)

5^(2x+4) = 5^(4x-4)

Equating exponents when base are same,

2x + 4 = 4x - 4

4x-2x = 4+4

2x = 8

=> x = 4

Thereby, the value of 'x' satisfying the given equation is x = 4.

Answer 2

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${(25)}^{x + 2} = {(5)}^{x - 4} {(125)}^{x}$

${(5)}^{2(x + 2)} = {(5)}^{x - 4} {(5)}^{3x}$

${(5)}^{2x + 4} = {(5)}^{x - 4 + 3x}$

${(5)}^{2x + 4} = {(5)}^{4x - 4}$

Equating the powers,

2x + 4 = 4x - 4

=> 2x = 8

=> x = 4