Question

If $a^2=logx$, $b^3=logy$ and $\frac{a^2}{2}-\frac{b^3}{3}=logc$, find c in terms of $x$ and $y$.

Answer 1

$a^2=logx$ , $b^3=logy$

$\frac{a^2}{2}-\frac{b^3}{3}=logc$

logx/3-logy/3=logc

$\frac{3logx-2logy}{6}$= log c

$3logx-2logy=6logc$

$log\frac{x^3}{y^2}$ =$log{c}^6$

$\frac{x^3}{y^2}$ =$c^6$​​​​​

c = 6$\sqrt{\frac{x^3}{y^2}}$