Question

Evaluate for x :
(√5/√3)⁽ˣ⁻⁸⁾ = (27/125)⁽²ˣ⁻³⁾

Answer 1

The value of x is 2

Step-by-step explanation:

Now, (√5 / √3)ˣ⁻⁸ = (27 / 125)²ˣ⁻³

or, {(5 / 3)^(1/2)}ˣ⁻⁸ = {(3/5)³}²ˣ⁻³

or, (5 / 3)^{(x - 8)/2} = (3 / 5)^{3 (2x - 3)}

or, (5 / 3)^(x/2 - 4) = (3 / 5)⁶ˣ⁻⁹

or, (5 / 3)^(x/2 - 4) / (3 / 5)⁶ˣ⁻⁹ = 1

or, (5 / 3)^(x/2 - 4) * (5 / 3)⁶ˣ⁻⁹ = 1

or, (5 / 3)^(x/2 - 4 + 6x - 9) = 1

or, (5 / 3)^(13x/2 - 13) = 1

Comparing from both sides, we write

13x/2 - 13 = 0, since a⁰ = 1

or, 13x/2 = 13

or, x = 13 * 2/13

or, x = 2

Therefore the required solution is x = 2