Question

Solve the equation for $x:\log 4+(1+\frac{1}{2x})\log 3=\log (\sqrt[3]{33}+27)$

Answer 1

$\log 4+(1+\frac{1}{2x})\log 3=\log (3^{1/3}+27)$

$\log (4\times 3^{(1+\frac{1}{2x})}).\log (3^{1/3}+27)$

$4\times 3^{(1+\frac{1}{2x})}=3^{1/3}+27$

$4\times 3\times 3^{1/2x}=3^{1/3}+27$

$3^{1/2x}=\frac{3^{1/3}+27}{12}$

$\frac{1}{2x}\log 3=\log \left(\frac{3^{1/3}+27}{12}\right)$

$x=\frac{\log 3}{2\log \left(\frac{3^{1/3}+27}{12}\right)}$