Question

(2^12-2x)=16 can you compute this?

Answer 1

The given equation is:

`2^(12-2x)=16`

Apply logarithm to both sides:

`\log 2^(12-2x)=\log 16`

Apply the properties of logarithms:

`(12-2x)\log 2=\log 16`

Divide both sides by log2:

`\begin{gathered} ((12-2x)\log2)/(\log2)=(\log 16)/(\log 2) \\ \text{Simplify} \\ 12-2x=(\log 16)/(\log 2) \end{gathered}`

And:

`\begin{gathered} \log _ax=(\log _bx)/(\log _ba) \\ \text{Then:} \\ (\log _(10)16)/(\log _(10)2)=\log _216=4 \end{gathered}`

Thus:

`\begin{gathered} 12-2x=4 \\ -2x=4-12 \\ -2x=-8 \\ x=(-8)/(-2) \\ x=4 \end{gathered}`

The answer is x=4.