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

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Solution

log a^2 = log x ⇒a^2 = x .........(Eq.1)

b^3 = log y ............... (Eq.2)

3a^2 - 2b^3 = 6 log z

Substituting a^2 & b^3 from Eq.1 & Eq.2

3x - 2 log y = 6 log z

3x = 2 log y + 6 log z
3x = log y^2 + log z^6 (Since a log b = log (b)^a )

3x = log (y^2 z^6 ) (Since log a + log b = log ab )

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