Question

If log ₃ m = x and log ₃ n = y, write down
`3^(1-2y+3x)` in terms of m an n

Answer 1

`3^(1-2y+3x)` in terms of m an n
log ₃ m = x
⇒ m = 3^x
log ₃ n = y
⇒ n = 3^y 
∴ `3^(1-2y+3x)`
= 3.3^-2y.3^3x
= 3.(3^y)^-2.(3^x)³ 
= 3n^-2.m³
= `(3"m"^3)/"n"^2`.