Question

Given: log₃ m = x and log₃ n = y.
Express 3^{2x - 3} in terms of m.

Answer 1

Given that log₃m = x and log₃n = y
⇒ 3^x = m and 3^y = n 

Consider the given expression :
3^{2x - 3}
= 3^2x . 3^-3
=` 3^(2x) . 1/3^3`

= `3^(2x)/3^3`

= `(3^x)^2/3^3`

= `m^2/27`
Therefore, 3^{2x - 3} = `m^2/27`