Solve the equation for x. 4⋅2x=32 Which answer shows the correct steps for solving the equation? Responses 4⋅2x2xlog22xxlog22x⋅00=32=8=log28=3=3≠3No solution 4⋅2x2xlog22xxlog22x⋅00=32=8=log28=3=3≠3No solution 4⋅2x2xlog22xxlog22x⋅1x=32=8=log28=3=3=3 4⋅2x2xlog22xxlog22x⋅1x=32=8=log28=3=3=3 4⋅2x2xlog22xxlog22x⋅1x=32=8=log28=4=4=4 4⋅2x2xlog22xxlog22x⋅1x=32=8=log28=4=4=4 4⋅2x8xlog88xxlog88x⋅1x=32=8=log88=1=1=1

The correct steps to solve the equation 4⋅2x = 32 are as follows:

Step 1: Divide both sides of the equation by 4 to isolate 2x. This gives us 2x = 8.

Step 2: To solve for x, we need to find the value that makes 2 raised to the power of x equal to 8. This is the same as solving the equation 2x = 8.

Step 3: We can solve this equation by taking the logarithm base 2 of both sides. This gives us x = log2(8).

Step 4: Evaluating log2(8) gives us x = 3.

So, the correct answer is the one that follows these steps. None of the provided responses exactly match these steps, but the closest one is the third response:

4⋅2x2xlog22xxlog22x⋅1x=32=8=log28=3=3=3

This response correctly isolates 2x, takes the logarithm base 2 of both sides, and solves for x. However, it incorrectly states that log2(8) = 4, when in fact log2(8) = 3. So, while this response is the closest to the correct steps, it contains an error in the final step.