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If log_2(x + 1) - log_2(x) = 1, what is the value of x?

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Question: If log_2(x + 1) - log_2(x) = 1, what is the value of x?

Options:

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  4. 4

Correct Answer: 1

Solution: 

log_2((x + 1)/x) = 1 implies (x + 1)/x = 2 => x + 1 = 2x => x = 1.

If log_2(x + 1) - log_2(x) = 1, what is the value of x?

Practice Questions

Q1
If log_2(x + 1) - log_2(x) = 1, what is the value of x?
  1. 1
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Questions & Step-by-Step Solutions

If log_2(x + 1) - log_2(x) = 1, what is the value of x?
Correct Answer: 1
  • Step 1: Start with the equation log_2(x + 1) - log_2(x) = 1.
  • Step 2: Use the property of logarithms that states log_a(b) - log_a(c) = log_a(b/c).
  • Step 3: Rewrite the equation as log_2((x + 1)/x) = 1.
  • Step 4: Convert the logarithmic equation to its exponential form: (x + 1)/x = 2.
  • Step 5: Multiply both sides by x to eliminate the fraction: x + 1 = 2x.
  • Step 6: Rearrange the equation to isolate x: x + 1 - x = 2x - x, which simplifies to 1 = x.
  • Step 7: Therefore, the value of x is 1.
  • Logarithmic Properties – Understanding the properties of logarithms, particularly the subtraction of logs leading to division.
  • Exponential Equations – Solving equations that involve exponentials derived from logarithmic expressions.
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