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\\) \\(\dots\\) rewrite the given equation without logarithms. do not solve for x. (do not simplify.)

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 of logarithms, we rewrite $\log_{2}x=4$ as $2^{4}=x$.

Answer:

$x = 2^{4}$ (or we can also write it as $2^{4}=x$)