Math Problem Statement

10^2=100 is equivalent to \log _(10) G=H.

Solution

The equation 102=10010^2 = 100 is indeed equivalent to a logarithmic form, where we rewrite the expression using a logarithm with base 10.

Given: 102=10010^2 = 100

This can be rewritten in logarithmic form as: log10100=2\log_{10} 100 = 2

To relate this to the format log10G=H\log_{10} G = H, we identify:

  • G=100G = 100
  • H=2H = 2

So, the equivalent expression is: log10100=2\log_{10} 100 = 2

Would you like more details, or do you have any further questions?

Related Questions

  1. What are some common properties of logarithms?
  2. How do we convert between exponential and logarithmic forms in general?
  3. Can logarithms have bases other than 10, and how does that change the interpretation?
  4. How would we evaluate log101000\log_{10} 1000 in a similar manner?
  5. What is the significance of log10\log_{10} (also called the common logarithm) in scientific calculations?

Tip

Remember, log10\log_{10} is often just written as log\log (without the base) because it’s commonly used in scientific contexts.

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Math Problem Analysis

Mathematical Concepts

Exponents
Logarithms

Formulas

10^2 = 100
\log_{10} G = H

Theorems

Properties of logarithms

Suitable Grade Level

Grades 7-9