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If log10(0.1) = z, what is the value of z?

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Question: If log10(0.1) = z, what is the value of z?

Options:

  1. -1
  2. 0
  3. 1
  4. 2

Correct Answer: -1

Solution: 

log10(0.1) = -1, so z = -1.

If log10(0.1) = z, what is the value of z?

Practice Questions

Q1
If log10(0.1) = z, what is the value of z?
  1. -1
  2. 0
  3. 1
  4. 2

Questions & Step-by-Step Solutions

If log10(0.1) = z, what is the value of z?
  • Step 1: Understand what log10 means. It is asking for the power to which 10 must be raised to get a certain number.
  • Step 2: We need to find log10(0.1). This means we want to know what power of 10 gives us 0.1.
  • Step 3: Rewrite 0.1 as a fraction. 0.1 can be written as 1/10.
  • Step 4: Recognize that 1/10 is the same as 10 raised to the power of -1. So, 0.1 = 10^(-1).
  • Step 5: Since log10(10^(-1)) = -1, we can conclude that log10(0.1) = -1.
  • Step 6: Therefore, if log10(0.1) = z, then z = -1.
  • Logarithms – Understanding the properties of logarithms, particularly how to evaluate logarithms of fractions and decimals.
  • Base 10 Logarithm – Recognizing that log10(x) represents the power to which 10 must be raised to obtain x.
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