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Solve the equations and check for extraneous solutions5^3^x + 14 = 78

Sagot :

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]