Question

If a² = log x, b³ = log y and 3a² - 2b³ = 6 log z, express y in terms of x and z .

Answer 1

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`