Question

Given: log₃ m = x and log₃ n = y.

Write down `3^(1 - 2y + 3x)` in terms of m and n.

Answer 1

log_⁡3m = x
log_3​n = y

3^1−2y+3x

Since log⁡₃m = x, then by definition of logarithms:

m = 3^x and n = 3^y

3^1−2y+3x = 3¹ ⋅ 3^−2y ⋅ 3^3x

Replace powers

3¹ = 3

3^3x = (3^x)³ = m³

3^−2y = (3^y)⁻² = n⁻²

3^1−2y+3x = 3 ⋅ n⁻² ⋅ m³ 

`3 . m^3/n^2`