Math Problem Statement

Rewrite the logarithmic expression as a single logarithm with the same base: log 2 - log 9

Solution

To rewrite the given expression log2log9\log 2 - \log 9 as a single logarithm, we can apply the logarithmic subtraction rule:

logb(a)logb(c)=logb(ac)\log_b(a) - \log_b(c) = \log_b\left(\frac{a}{c}\right)

For the expression log2log9\log 2 - \log 9, we apply the rule:

log(29)\log \left(\frac{2}{9}\right)

Thus, the expression simplifies to:

log29\log \frac{2}{9}

Would you like further details on this topic? Here are five related questions:

  1. How do you combine multiple logarithmic expressions into a single logarithm?
  2. What happens when you add two logarithms with the same base?
  3. How can the properties of logarithms simplify complex logarithmic expressions?
  4. What is the reverse process of combining logarithms (expanding)?
  5. How do you apply logarithms to solve exponential equations?

Tip: Always remember to check the base of the logarithms before combining them!

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Math Problem Analysis

Mathematical Concepts

Logarithms
Properties of Logarithms

Formulas

log_b(a) - log_b(c) = log_b(a/c)

Theorems

Logarithmic Subtraction Rule

Suitable Grade Level

Grades 9-12