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If log_10(0.01) = x, what is the value of x?

Practice Questions

Q1
If log_10(0.01) = x, what is the value of x?
  1. -1
  2. -2
  3. -3
  4. -4

Questions & Step-by-Step Solutions

If log_10(0.01) = x, what is the value of x?
  • Step 1: Understand that log_10 means 'logarithm base 10'.
  • Step 2: Rewrite 0.01 as a power of 10. Since 0.01 is the same as 10 raised to the power of -2, we can write it as 0.01 = 10^-2.
  • Step 3: Substitute 10^-2 into the logarithm: log_10(0.01) becomes log_10(10^-2).
  • Step 4: Use the property of logarithms that says log_b(b^a) = a. Here, b is 10 and a is -2.
  • Step 5: Therefore, log_10(10^-2) = -2.
  • Step 6: Conclude that x = -2.
  • Logarithmic Properties – Understanding how to manipulate logarithms, particularly the property that log_b(a^c) = c * log_b(a).
  • Base 10 Logarithm – Recognizing that log_10 is the logarithm with base 10, which is commonly used in calculations involving powers of 10.
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