Question

Which of the following is the solution to the equation?

Answer 1

`2\cdot3^{(2x)/(7)}=30`

To solve x:

1. Divide both sides of the equation into 2:

`\begin{gathered} \frac{2\cdot3^{(2x)/(7)}}{2}=(30)/(2) \\ \\ 3^{(2x)/(7)}=15 \end{gathered}`

2. Use the next property to convert the exponent into a logarithm:

`\begin{gathered} a^x=y \\ x=\log _ay \end{gathered}`
`(2x)/(7)=\log _3(15)`

3. Multiply both sides of the equation by 7/2:

`\begin{gathered} (7)/(2)\cdot(2x)/(7)=(7)/(2)\log _3(15) \\ \\ x=(7)/(2)\log _3(15) \end{gathered}`

Then, the solution for the given equation is:

`x=(7)/(2)\log _3(15)`