Question

If $a^2=\log x,b^3=\log y$ and $3a^2-2b^3=6\log z$, then express $y$ in terms of $x$ and $z$

• A. $y=x^{\frac{3}{2}}÷z^5$
• B. $y=x^{\frac{2}{3}}÷z^3$
• C. $y=x^{\frac{3}{2}}÷z^3$
• D. $y=x^{\frac{3}{2}}÷z^2$

Answer 1

Answer: (C)

$y=x^{\frac{3}{2}}÷z^3$

$a^2=\log x,b^3=\log y$
$3a^2-2b^3=6\log z$
$x={10}^{a^2},y={10}^{b^3},z={10}^{\frac{1}{6}(3a^2-2b^3)}$ ...(1)
$\therefore z=\frac{{10}^{a^2/2}}{{10}^{b^3/3}}$ ...(2)
From 1 and 2 we get
$\therefore z=\frac{x^{\frac{1}{2}}}{y^{\frac{1}{3}}}$ and $y=\frac{x^{\frac{3}{2}}}{z^3}$