Questions: Solve the following logarithmic equation. log2(x+3)=log28 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. Type an exact answer. Use a comma to separate answers as needed.) B. There is no solution.

Solve the following logarithmic equation.
log2(x+3)=log28

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. Type an exact answer. Use a comma to separate answers as needed.)
B. There is no solution.

Transcript text: Solve the following logarithmic equation. \[ \log _{2}(x+3)=\log _{2} 8 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\square$ \}. (Simplify your answer. Type an exact answer. Use a comma to separate answers as needed.) B. There is no solution.

Solution

Solution Steps

Step 1: Set the Arguments Equal

Given the logarithmic equation: \[ \log_{2}(x + 3) = \log_{2}(8) \] Since the bases are the same, we can set the arguments equal to each other: \[ x + 3 = 8 \]

Step 2: Solve for $ x $

To isolate $ x $, we subtract 3 from both sides: \[ x = 8 - 3 \] This simplifies to: \[ x = 5 \]

Step 3: Write the Solution Set

The solution set is: \[ \{5\} \]