Question

Which of the following is the solution to the equation?

Answer 1

$2\cdot3^{\frac{2x}{7}}=30$

To solve x:

1. Divide both sides of the equation into 2:

$\begin{gathered} \frac{2\cdot3^{\frac{2x}{7}}}{2}=\frac{30}{2} \\ \\ 3^{\frac{2x}{7}}=15 \end{gathered}$

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

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

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

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

Then, the solution for the given equation is:

$x=\frac{7}{2}\log _3(15)$