Math Problem Statement

Convert to Logarithmic Form: 10^{-2} = 0.01

Solution

To convert the equation 102=0.0110^{-2} = 0.01 to its logarithmic form, we apply the logarithmic definition. The general rule for converting an exponential equation to logarithmic form is:

ab=cis equivalent tologa(c)=ba^b = c \quad \text{is equivalent to} \quad \log_a(c) = b

In your case:

  • The base aa is 10.
  • The exponent bb is 2-2.
  • The result cc is 0.010.01.

So, the logarithmic form of the equation 102=0.0110^{-2} = 0.01 is:

log10(0.01)=2\log_{10}(0.01) = -2

Would you like further details on logarithmic transformations or examples?

Here are 5 related questions to further explore the concept:

  1. How do you convert a general logarithmic equation back into exponential form?
  2. What are the properties of logarithms that simplify complex expressions?
  3. What is the logarithmic value of 1 for any base? Why is it special?
  4. How can you solve logarithmic equations with unknown variables?
  5. What is the relationship between natural logarithms and common logarithms?

Tip: Logarithms with a base of 10 are called common logarithms and are often used in scientific calculations due to their convenience with powers of 10.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponents
Base 10

Formulas

a^b = c is equivalent to log_a(c) = b

Theorems

Logarithmic and Exponential Equivalence

Suitable Grade Level

Grades 8-10