Question

Please help. I get until making the fraction bav into root.

Answer 1

We need to solve the following equation:

`4^3=2^{(3)/(2)x}`

For that we need to isolate the x variable on the left side of the equation, since the variable is on the exponent of the power we need to first remove it from there. To do that we will use logarithms, the first step is to make sure both sides have the same base. This is done below:

`\begin{gathered} (2^2)^3=2^{(3)/(2)x} \\ 2^6=2^{(3)/(2)x} \end{gathered}`

Now that both sides have the same base we can apply a logarithm on both sides with the same base as the powers. This is done below:

`\log _22^6=\log _22^{(3)/(2)x}`

Since the log and the power have the same base we can cancel the logs and the power as shown below:

`\begin{gathered} 6\cdot\log _22=(3)/(2)x\cdot\log _22 \\ 6=(3)/(2)x \\ (3)/(2)x=6 \\ 3x=2\cdot6 \\ 3x=12 \\ x=(12)/(3) \\ x=4 \end{gathered}`

The correct answer is 4.