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If log_2(x + 1) - log_2(x) = 1, what is the value of x?
If log_2(x + 1) - log_2(x) = 1, what is the value of x?
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If log_2(x + 1) - log_2(x) = 1, what is the value of x?
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log_2((x + 1)/x) = 1 implies (x + 1)/x = 2 => x + 1 = 2x => x = 1.
Questions & Step-by-step Solutions
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Q: If log_2(x + 1) - log_2(x) = 1, what is the value of x?
Solution:
log_2((x + 1)/x) = 1 implies (x + 1)/x = 2 => x + 1 = 2x => x = 1.
Steps: 7
Show Steps
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.
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