If Log X = P + Q and Log Y = P - Q, Find the Value of Log 10 X Y 2 in Terms of P and Q. - Mathematics

If log x = p + q and log y = p - q, find the value of log `(10x)/y^2` in terms of p and q.

Sum

log x = p + q and log y = p - q
`"log"(10x)/y^2` = log 10x - log y²

⇒ `"log"(10x)/y^2` = log10 + logx - 2logy

⇒ `"log"(10x)/y^2` = 1 + p + q - 2(p - q)

⇒ `"log"(10x)/y^2` = 1 - p + 3q.

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Expansion of Expressions with the Help of Laws of Logarithm

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Chapter 10: Logarithms - Exercise 10.2

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