Question

5^(x-3) × 3^(2x-3)= 225

Answer 1

aloha user!!


we are given this equation.
we have to find the value of x.

5^(x-3) × 3^(2x-3)= 225

we are going to break down 225 by prime factorization first.

5^(x-3) × 3^(2x-3) = 5 × 5  × 3 × 3

5^(x-3) × 3^(2x-3) = 5² × 3²

so clearly we see x-3 must be equal to 2 and 2x-3 must be equal to 2.

x-3=2
x=2+3
x=5

now,

2x-3=2
2x=2+3
x= 5/2


hope it helps !!

good life !!