Evaluating Logs & Derivatives: More Questions Answered Here

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Discussion Overview

The discussion revolves around evaluating logarithmic expressions and derivatives, specifically focusing on problems involving logarithms with exponents and the differentiation of functions. Participants seek clarification on their answers and methods for solving these mathematical problems.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses frustration with logarithm questions not covered in their coursework and requests help with specific problems.
  • Another participant seeks clarification on the interpretation of a logarithmic expression, questioning whether it should be treated as \((\log_{2}2)^{\log_{5}5}\) or \(\log_{2}(2)^{\log_{5}5}\).
  • A different participant notes that \(\log_{5}5\) equals 1 and provides a transformation of a logarithmic equation involving \(x\) to simplify it.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of the logarithmic expression, and there are varying approaches to solving the problems presented. The discussion remains unresolved regarding the correct methods and answers.

Contextual Notes

Some participants express uncertainty about the application of logarithmic properties and derivatives, indicating potential gaps in their understanding of the material. The lack of brackets in the original expression leads to ambiguity in interpretation.

m0286
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Can some one check my answers please?

The answers are in my reply post at the bottom of this page THANKS :smile:


I have a couple more log questions I am stuck on. They keep giving me log questions that they never showed me how to do.. very fustrating!
I need to evaluate the following logarithms:

68 a). log22^log55
I don't even know where to begin.. I never done a log with an exponent log?

69. log25=log2(x+32)-log2x

Determine the derivative of:
70 c) y= 2x^3 e^4x

e) y= square root(x^3 + e^-x +5)
I know this one should probably go to. (x^3 + e^-x +5)^1/2... then,
dy/dx= (x^3 + e^-x +5)^1/2 * 1/2(x^3 + e^-x +5)^-1/2 * (3x^2)now I am confused? does the e^-x have a derivative?? like -xe^-2?? i got no idea.
CAN ANYONE HELP ME PLEASE...
THANKZ YA!
 
Last edited:
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For part a, is that

[tex](\log_{2}2)^{\log_{5}5}[/tex] or [tex]\log_{2}(2)^{\log_{5}5}[/tex]?
 
umm there are no brackets, but i think the 2 is in part with the log2
 
Hrm

[tex]\log_{5} 5 = 1[/tex]

[tex]5^1 = 5[/tex]

[tex]log_{2} 5= log_{2} (x+32) - log_{2} x[/tex]

[tex]log_{2} 5= log_{2} \frac{x+32}{x}[/tex]

[tex]5 = \frac{x+32}{x}[/tex]
 
Last edited:

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