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Question
If a2 = log x , b3 = log y and `a^2/2 - b^3/3` = log c , find c in terms of x and y.
Solution
Given a2 = log x , b3 = log y
Now `a^2/2 - b^3/3` = log c
⇒ `log x/2 - log y/3 = log c`
⇒ `[ 3log x - 2log y]/6 = log c`
⇒ 3log x - 2log y = 6log c
⇒ log x3 - logy2 = 6log c
⇒ `log(x^3/y^2) = logc^6`
⇒ `x^3/y^2 = c^6`
⇒ c = `root(6)( x^3/y^2 )`
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