Math Problem Statement

log4/log2

Solution

The expression log4log2\frac{\log 4}{\log 2} can be simplified using the properties of logarithms, specifically the change of base formula:

log4log2=log24\frac{\log 4}{\log 2} = \log_2 4

Now, log24\log_2 4 asks the question: "To what power must 2 be raised to get 4?" Since 22=42^2 = 4, we have:

log24=2\log_2 4 = 2

Therefore:

log4log2=2\frac{\log 4}{\log 2} = 2

Would you like more details or have any questions?

Here are some related questions:

  1. What is the value of log28\log_2 8?
  2. How can you simplify log16log4\frac{\log 16}{\log 4}?
  3. What is the general form of the change of base formula for logarithms?
  4. How do you simplify log32log2\frac{\log 32}{\log 2}?
  5. What is the result of log39\log_3 9?

Tip: Remember that logab=logcblogca\log_a b = \frac{\log_c b}{\log_c a} for any positive base cc.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Change of Base Formula

Formulas

Change of base formula: \(\log_a b = \frac{\log_c b}{\log_c a}\)

Theorems

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Suitable Grade Level

Advanced High School