Question

Solve for x

(1/3)^(x−2)=9^(x−3)

Answer 1

(1/3)^(x−2)  =  9^(x−3)

[3^(-1)]^(x−2)  =  [3^2]^(x−3)

3^[(-1)(x−2)]  =  3^[2(x−3)]

3^(-x + 2)  =  3^(2x − 6)

As the bases are the same equate the exponents

- x + 2  =  2x - 6

2x + x  =  2 + 6

3x  =  8

x  =  8/3

Answer :

The solution is x  =  8/3.