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प्रश्न
If a2 = log x, b3 = log y and 3a2 - 2b3 = 6 log z, express y in terms of x and z .
उत्तर
Given that
a2 = log x, b3 = log y and 3a2 - 2b3 = 6 log z
Consider the equation,
3a2 - 2b3 = 6log z
⇒ 3log x - 2log y = 6log z
⇒ logx3 - logy2 = logz6
⇒ log `(x^3/y^2)` = logz6
⇒ `x^3/y^2 = z^6`
⇒ `x^3/z^6 = y^2`
⇒ `y^2 = x^3/z^6`
⇒ y = `( x^3/z^6 )^(1/2)`
⇒ y = `( x^(3/2)/z^(6/2))`
⇒ y = `x^(3/2)/z^3`
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