(Solved): (a) Solve the following expression for \( x \), showing all steps: \[ \frac{125^{\frac{1}{3}}+\frac ...

(a) Solve the following expression for \( x \), showing all steps: \[ \frac{125^{\frac{1}{3}}+\frac{11}{2}}{3}=-\frac{14}{3}+\frac{x^{\frac{2}{3}}}{24} \] (b) Use \( \log \) rules to show step by step that \[ \log \left(\frac{x^{3} y^{4}}{e^{5} z^{2}}\right) \] is equivalent to \[ 3 \log (x)+4 \log (y)-2 \log (z)-5 \]