Given that log m x^2(y) = n and log m x/(y)2 = p, express log m x/y in terms of n and p.?

It’s indices and logarithms. Please help. TQ.

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A few days ago

Anonymous

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log(m) (x^2 y) = n

log(m) ( x/ y^2 ) = p

From the definition of a logarithm to base m:

x^2 y = m^n …(1)

x / y^2 = m^p …(2)

Squaring (1):

x^4 y^2 = m^(2n) …(3)

Multiplying (3) by (2):

x^5 = m^(2n + p)

Taking 5th root:

x = m^( (2n + p)/5 ).

Squaring (2):

x^2 / y^4 = m^(2p)

Raising to power (-1):

y^4 / x^2 = m^(-2p)

Multiplying by (1):

y^5 = m^(n – 2p)

Taking 5th root:

y = m^( (n – 2p)/5 ).

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