Question

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

Answer 1

Answer:

x = 17/7

Step-by-step explanation:

Given-

$(\frac{5}{3} )^{x - 8}$ = $( \frac{27}{125} ) ^{2 x - 3}$

$(\frac{5}{3} )^{x - 8}$ = $((\frac{3}{5} ) ^{3}) ^{2 x - 3}$

$(\frac{5}{3} )^{x - 8}$ = $(( \frac{5}{3} ) ^{(-3)})^{2 x - 3}$

$(\frac{5}{3} )^{x - 8}$  = $(\frac{5}{3} )^{ - 6 x + 9}$

On comparing both sides-

x - 8 = - 6 x + 9

7 x = 17

x = 17/7

∴ x = 17/7.