SOLUTION: Given that {{{log (x^2y) = n}}} and {{{log (x/y^2) = p}}}, express {{{log (x/y)}}} in terms of n and p. NOTE THAT THE BASE OF THE LOGARITHM is m.

Question 1138426: Given that and , express in terms of n and p.
NOTE THAT THE BASE OF THE LOGARITHM is m.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

(1)

(2)

(1) and (2) are a pair of linear equation with log(x) and log(y) as the variables. Solve the pair of equations for log(x) and log(y) in terms of n and p.

(3) [equation (1), multiplied by 2]
[equation (2) plus equation (3)]

(4) [equation (2), multiplied by -2]
[equation (1) plus equation (4)]

Now we have expressions for log(x) and log(y) in terms of n and p, so we can find an expression for log(x/y) in terms of n and p.

ANSWER:

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