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If log2(x) + log2(8) = 7, what is the value of x?

Practice Questions

Q1
If log2(x) + log2(8) = 7, what is the value of x?
  1. 32
  2. 64
  3. 128
  4. 256

Questions & Step-by-Step Solutions

If log2(x) + log2(8) = 7, what is the value of x?
Correct Answer: 16
  • Step 1: Start with the equation: log2(x) + log2(8) = 7.
  • Step 2: Recognize that log2(8) can be simplified. Since 8 is 2 raised to the power of 3, log2(8) = 3.
  • Step 3: Substitute log2(8) with 3 in the equation: log2(x) + 3 = 7.
  • Step 4: To isolate log2(x), subtract 3 from both sides: log2(x) = 7 - 3.
  • Step 5: Calculate the right side: log2(x) = 4.
  • Step 6: To find x, rewrite the equation in exponential form: x = 2^4.
  • Step 7: Calculate 2^4, which equals 16.
  • 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 using the relationship between logarithms and exponents.
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