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Question
Given: log3 m = x and log3 n = y.
Write down `3^(1 - 2y + 3x)` in terms of m and n.
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Solution
log3m = x
log3n = y
31−2y+3x
Since log3m = x, then by definition of logarithms:
m = 3x and n = 3y
31−2y+3x = 31 ⋅ 3−2y ⋅ 33x
Replace powers
31 = 3
33x = (3x)3 = m3
3−2y = (3y)−2 = n−2
31−2y+3x = 3 ⋅ n−2 ⋅ m3
`3 . m^3/n^2`
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