Math Problem Statement
Let \log_{b}\left(2\right)=p $$$$ \log_{b}\left(3\right)=q $$$$ \log_{b}\left(5\right)=r. Express in terms of p, q, or r
Solution
To express in terms of , , and , we can use the change of base formula, which states:
Here, we want to express . Using the change of base formula:
We know that and , so we have:
Thus, the expression for in terms of is:
Would you like further details or have any questions?
Here are 5 related questions you might find interesting:
- How can be expressed in terms of and ?
- What is the relationship between and , , and ?
- How would you express in terms of , , and ?
- Can you express in terms of and ?
- How do you find using and the change of base formula?
Tip: When solving logarithmic problems, the change of base formula is a powerful tool for converting logs to different bases, allowing for easier manipulation and comparison of logarithmic expressions.
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Math Problem Analysis
Mathematical Concepts
Logarithms
Change of Base Formula
Formulas
Change of base formula: \(\log_a(c) = \frac{\log_b(c)}{\log_b(a)}\)
Theorems
-
Suitable Grade Level
High School
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