Question

If $a^2=\log x,b^3=\log yand\frac{a^2}{2}-\frac{b^3}{3}=\log c$

Answer 1

$a^2=\log x,b^3=\log y$

Now

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

$\Rightarrow \frac{\log x}{2}-\frac{\log y}{3}=\log c$

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

$\Rightarrow 3\log x-2\log y=6\log c$

$\Rightarrow \log x^3-\log y^2=6\log c$

$\Rightarrow \log \left(\frac{x^3}{y^2}\right)=\log c^6$

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

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