Question

solve the following logarithmic equation. be sure to reject any value of x that is not in the domain of the original logarithmic expression. give the exact answer. \\(\log_{2} x = 4\\) rewrite the given equation without logarithms. do not solve for x. \\(2^{4}=x\\) (do not simplify.) solve the equation. select the correct choice below and, if necessary, fill in the answer box to complete your choice. \\(\bigcirc\\) a. the solution set is \\(\\{\quad\\}\\). (simplify your answer.) \\(\bigcirc\\) b. there are infinitely many solutions. \\(\bigcirc\\) c. there is no solution.

Explanation:

Step1: Recall the logarithmic definition

The logarithmic equation \(\log_{a}b = c\) can be rewritten in exponential form as \(a^{c}=b\). Here, \(a = 2\), \(b=x\), and \(c = 4\).

Step2: Apply the definition

Using the definition, we rewrite \(\log_{2}x=4\) as \(2^{4}=x\).

Answer:

\(2^{4}=x\) (which simplifies to \(x = 16\), but as per the instruction not to simplify, the rewritten form is \(2^{4}=x\))