41. If log xy^3 = m and log xy^2 = p, find log (x^2 + y)
in terms of m and p.
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Answer:
-4mp log 10^7p + 10^5m
Step-by-step explanation:
log xy³ = m=> (1)
log xy² = p => (2)
(1)-(2)
log xy³/xy² = m -p
log y = m-p
10^(m-p) = y
putting this in (2)
log xy² = p
log x + log y² = p
log x +log 10^(2m-2p) = p
log x + 2m -2p = p
log x = 3p -2m
x = 10^(3p-2m)
Now , main part :
log (x²+y)
log {10^(6p-4m )} + 10^(m-p)
-4mp log 10^7p + 10^5m
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