Question

Which equation can be used to find the solution of (1/2)2x=32

Answer 1

Notice that:

`\begin{gathered} ((1)/(2))^(2x)=(2^(-1))^(2x)=2^(-2x), \\ 32=2^5\text{.} \end{gathered}`

Therefore:

`2^(-2x)=2^5\text{.}`

Now, applying the logarithm base 2 to the above equation we get:

`\begin{gathered} \log _2(2^(-2x))=\log _22^5\text{.} \\ \end{gathered}`

Now, recall that:

`\log _bb^m=m\text{.}`

Therefore:

`-2x=5.`

Answer: Last option.

`-2x=5.`