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.

Answer 1

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 )`