How can Pete solve a logarithmic problem using the Change of Base Formula?

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Discussion Overview

The discussion revolves around how Pete can solve a logarithmic problem using the Change of Base Formula, specifically focusing on the expression x^(log base x of y). The scope includes conceptual understanding of logarithms and their properties, as well as the application of the Change of Base Formula.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Main Points Raised

  • Pete is trying to solve the equation x^(log base x of y) and is seeking guidance on how to approach it using the Change of Base Formula.
  • Some participants clarify the definition of a logarithm, stating that log base b of n = x is equivalent to b^x = n.
  • One participant introduces a variable ξ to represent log_x y, suggesting that x^ξ = y, and asks how to proceed from this point.
  • A later reply expresses gratitude for the clarification on the cancel-out rule, indicating a desire for deeper understanding of the underlying principles.

Areas of Agreement / Disagreement

The discussion appears to be exploratory with no clear consensus or resolution on how to solve the problem, as participants are sharing definitions and seeking clarification rather than agreeing on a specific method.

Contextual Notes

Participants have not fully resolved the mathematical steps involved in applying the Change of Base Formula to the problem presented, and there may be assumptions regarding prior knowledge of logarithmic properties that are not explicitly stated.

Who May Find This Useful

Individuals interested in understanding logarithmic functions, the Change of Base Formula, and those seeking clarification on mathematical reasoning related to logarithms may find this discussion beneficial.

Helicobacter
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Pete has access to a scientific calculator and only knows the Definition of a Logarithm and the Change of Base Formula. How is Pete able to solve the following problem?:

x^(log base x of y) =
 
Last edited:
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What is the definition of a logarithm ?
 
log base b of n = x <=> b^x = n
 
Let
[tex]\xi = \log_x y[/tex]
[tex]\Leftrightarrow x ^ {\xi} = y[/tex], right?
So:
[tex]x ^ {\log_x y} = x ^ {\xi} = ?[/tex]
Can you go from here? :)
 
Thanks! (Previously I knew the cancel-out-rule, but I didn't understand why you can cancel.)
 

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