A few days ago
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
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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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