Question

Evaluate for x:
(5/3)^x-8 = (27/125)^2x-3
Please and thank you!!

Answer 1

x = 17/7

Explanation:

Given-

`((5)/(3) )^(x - 8)` =
`( (27)/(125) ) ^(2 x - 3)`

`((5)/(3) )^(x - 8)` =
`(((3)/(5) ) ^(3)) ^(2 x - 3)`

`((5)/(3) )^(x - 8)` =
`(( (5)/(3) ) ^((-3)))^(2 x - 3)`

`((5)/(3) )^(x - 8)` =
`((5)/(3) )^( - 6 x + 9)`

On comparing both sides-

x - 8 = - 6 x + 9

7 x = 17

x = 17/7

∴ x = 17/7.