Question

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

Answer 1

we have the equation

`(5^3)^x+14=78`

Solve for x

`\begin{gathered} (5^3)^x=78-14 \\ (5^3)^x=64 \end{gathered}`

Applying log on both sides

`log((5^3)^x=log(64)`
`\begin{gathered} xlog(5^3)^=log(64) \\ x=(log64)/(2log5) \end{gathered}`