Solve the following logarithmic equation. Be sure to reject any value of that is not in the domain of the
original logarithmic expression. Give the exact answer.
Rewrite the given equation without logarithms. Do not solve for

(Do not simplify.)
Solve the equation. Select the correct choice below and, if necessary, fill in the answer box to complete your
choice.
A. The solution set is . (Simplify your answer.)
B. There are infinitely many solutions.
C. There is no solution.

Ask by Barrett Wheeler. in the United States

Mar 31,2025

Question

Solve the following logarithmic equation. Be sure to reject any value of that is not in the domain of the
original logarithmic expression. Give the exact answer.
Rewrite the given equation without logarithms. Do not solve for

(Do not simplify.)
Solve the equation. Select the correct choice below and, if necessary, fill in the answer box to complete your
choice.
A. The solution set is . (Simplify your answer.)
B. There are infinitely many solutions.
C. There is no solution.

Ask by Barrett Wheeler. in the United States

Mar 31,2025

UpStudy AI · Accepted Answer

Given the logarithmic equation

$$
\log_{2}(x)=2,
$$

we first note that the domain requires

$$
x>0.
$$

Step 1. Rewrite the equation in exponential form:

$$
x=2^{2}.
$$

Step 2. Simplify $$ 2^{2} $$:

$$
2^{2}=4.
$$

Step 3. Check the domain: Since $$4>0$$, the value is valid.

Thus, the solution set is

$$
\{4\}.
$$

The correct choice is A.
The solution set is {4}.