Question

solve for x : 5^-3x :5^x+7 = 1: 125​

Answer 1

Step-by-step explanation:

5^-3x : 5^x+7 = 1 : 125

5^-3x : 5^x+7 = 1 : (5)³

Cross multiply them.

5^-3x+3=5^x+7

Bases are equal, powers will be equal too.

-3x+3 = x+7

-3x-x = 7-3

-4x = 4

x= -1

Answer 2

Given :  5⁻³ˣ : 5ˣ⁺⁷ = 1: 125

To Find : Solve for x

Solution:

5⁻³ˣ : 5ˣ⁺⁷ = 1: 125

=> 5⁻³ˣ /  5ˣ⁺⁷   = 1/125

xᵃ/xᵇ = = xᵃ⁻ᵇ =  1/xᵇ⁻ᵃ  

=> 1/5ˣ⁺⁷⁻⁽⁻³ˣ⁾ = 1/5³

=>  1/5⁴ˣ⁺⁷ = 1/5³

=> 4x + 7 = 3

=> 4x = - 4

=> x = - 1

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