How Do You Estimate Logarithms Using Basic Logarithmic Properties?

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Homework Help Overview

The discussion revolves around estimating logarithmic values, specifically log(4), log(5), log(6), and log(8), using given approximations for log(2) and log(∏). Participants explore various logarithmic properties and relationships to derive these estimates.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss using logarithmic properties such as the product and quotient rules. There is an attempt to estimate log(5) through linear interpolation based on log(4) and log(6). Some participants also suggest alternative methods and hints related to logarithmic identities.

Discussion Status

The discussion is active with various approaches being explored. Some participants have provided hints and alternative methods, while others are questioning the assumptions made in the problem statement. No explicit consensus has been reached on the best approach for estimating log(5).

Contextual Notes

There is a mention of potential confusion regarding the problem statement, indicating that participants are considering whether the provided values and relationships are accurate or complete.

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Homework Statement


Given that log(2) is roughly 0.30 and log(∏) is roughly 0.5, estimate the values of log(4), log(5), log(6) and log(8).


Homework Equations


log(ab)=log(a)+log(b)
log(a/b)=log(a)-log(b)
log(a^n)=nlog(a)


The Attempt at a Solution


I found log(4) and log(8) using log(2)+log(2) [+log(2)], and i estimated log(6) using log(2)+log(∏), but i don't know how to get to log(5).
 
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hi k3r0! :smile:

hint: log(125) ? :wink:
 
My guess, assuming there isn't a mistake in the problem statement, is that they want you to use linear interpolation. log(5) ≈ (1/2)(log(4) + log(6)). This would be the average (or mean) of the two log values.
 
Mark44 said:
My guess, assuming there isn't a mistake in the problem statement, is that they want you to use linear interpolation. log(5) ≈ (1/2)(log(4) + log(6)). This would be the average (or mean) of the two log values.

Thanks a lot, that method never crossed my mind. I spent about half an hour being irritated at that question, haha.

Thanks!
 
another hint: what is \pi^2 equal to?
 
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log(5)=log(10)-log(2) = 1 - log(2) = 0.7
 

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