we have the equation
[tex](5^3)^x+14=78[/tex]Solve for x
[tex]\begin{gathered} (5^3)^x=78-14 \\ (5^3)^x=64 \end{gathered}[/tex]Applying log on both sides
[tex]log((5^3)^x=log(64)[/tex][tex]\begin{gathered} xlog(5^3)^=log(64) \\ x=\frac{log64}{2log5} \end{gathered}[/tex]