Math Problem Statement

Evaluate log 0.000 01

Solution

To evaluate the logarithm log(0.00001)\log(0.00001), we proceed as follows:

  1. Express the number in scientific notation:
    0.00001=1050.00001 = 10^{-5}.

  2. Apply the logarithm property:
    log(105)=5log(10).\log(10^{-5}) = -5 \cdot \log(10).

  3. Simplify:
    Since log(10)=1\log(10) = 1, log(105)=5.\log(10^{-5}) = -5.

So, log(0.00001)=5\log(0.00001) = -5.

The correct answer is 5-5.

Would you like more details or have any questions?

Here are 8 related questions for further practice:

  1. Evaluate log(0.001)\log(0.001).
  2. Find the value of log(100)\log(100).
  3. Calculate log(0.01)\log(0.01).
  4. What is log(1)\log(1)?
  5. Solve for xx in the equation log(x)=2\log(x) = 2.
  6. Evaluate log(1000)\log(1000).
  7. Determine the value of log(0.0001)\log(0.0001).
  8. What is the value of log(107)\log(10^{-7})?

Tip: Remember that the logarithm of a number in the form of 10n10^n simplifies to just nn, as log(10n)=n\log(10^n) = n.

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Math Problem Analysis

Mathematical Concepts

Logarithms

Formulas

\( \log(ab) = \log(a) + \log(b) \)
\( \log \left( \frac{a}{b} \right) = \log(a) - \log(b) \)
\( \log(a^b) = b \cdot \log(a) \)

Theorems

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Suitable Grade Level

Grades 10-12