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If log10(x) + log10(10) = 2, what is the value of x?

Practice Questions

Q1
If log10(x) + log10(10) = 2, what is the value of x?
  1. 10
  2. 100
  3. 1000
  4. 10000

Questions & Step-by-Step Solutions

If log10(x) + log10(10) = 2, what is the value of x?
Correct Answer: 10
  • Step 1: Start with the equation: log10(x) + log10(10) = 2.
  • Step 2: Recognize that log10(10) equals 1 because 10 raised to the power of 1 is 10.
  • Step 3: Substitute 1 for log10(10) in the equation: log10(x) + 1 = 2.
  • Step 4: To isolate log10(x), subtract 1 from both sides: log10(x) = 2 - 1.
  • Step 5: Simplify the right side: log10(x) = 1.
  • Step 6: Convert the logarithmic equation to exponential form: x = 10^1.
  • Step 7: Calculate 10^1, which equals 10.
  • Logarithmic Properties – Understanding the properties of logarithms, specifically that log(a) + log(b) = log(ab) and log(10) = 1.
  • Solving Logarithmic Equations – The ability to isolate the variable in a logarithmic equation and convert it back to exponential form.
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