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If log_2(x) + log_2(4) = 5, what is the value of x? (2023)

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Question: If log_2(x) + log_2(4) = 5, what is the value of x? (2023)

Options:

  1. 16
  2. 8
  3. 4
  4. 2

Correct Answer: 16

Exam Year: 2023

Solution: 

log_2(x) + 2 = 5 implies log_2(x) = 3, thus x = 2^3 = 8.

If log_2(x) + log_2(4) = 5, what is the value of x? (2023)

Practice Questions

Q1
If log_2(x) + log_2(4) = 5, what is the value of x? (2023)
  1. 16
  2. 8
  3. 4
  4. 2

Questions & Step-by-Step Solutions

If log_2(x) + log_2(4) = 5, what is the value of x? (2023)
  • Step 1: Start with the equation log_2(x) + log_2(4) = 5.
  • Step 2: Recognize that log_2(4) is equal to 2 because 2^2 = 4.
  • Step 3: Substitute 2 for log_2(4) in the equation: log_2(x) + 2 = 5.
  • Step 4: To isolate log_2(x), subtract 2 from both sides: log_2(x) = 5 - 2.
  • Step 5: Simplify the right side: log_2(x) = 3.
  • Step 6: Convert the logarithmic equation to exponential form: x = 2^3.
  • Step 7: Calculate 2^3, which equals 8.
  • Step 8: Therefore, the value of x is 8.
  • Logarithmic Properties – Understanding how to manipulate logarithmic equations, including the property that log_b(a) + log_b(c) = log_b(a*c).
  • Exponential Equations – Solving for x in equations involving exponents, particularly converting logarithmic results back to exponential form.
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