Why Does the Equation log(35-x^3)/log(5-x)=3 Simplify to 1000=(35-x^3)/(5-x)?

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Homework Help Overview

The discussion revolves around the equation log(35-x^3)/log(5-x)=3 and its simplification to 1000=(35-x^3)/(5-x). Participants are exploring logarithmic properties and their implications in solving the equation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to manipulate the logarithmic equation and question the validity of the steps taken. Some suggest using properties of logarithms to rewrite the equation, while others express confusion about the initial transformation.

Discussion Status

The discussion is active, with participants providing different perspectives on how to approach the logarithmic equation. Some guidance has been offered regarding the use of anti-logarithms and logarithmic identities, but no consensus has been reached on the best method to proceed.

Contextual Notes

There is a mention of potential misunderstandings regarding logarithmic properties, specifically in relation to the manipulation of the equation. Participants are also navigating the implications of their assumptions about the logarithmic functions involved.

thomasrules
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log(35-x^3)/log(5-x)=3

I can't get it...

What I did was: 1000=(35-x^3)/(5-x)
 
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Putting this in a better grouping you get [tex]3log(5-x)=log(35-x^{3})[/tex]

Take the anti-log of both sides from there.
 
Last edited by a moderator:
[tex]\frac {\ln x} {\ln y} \neq \ln ( \frac x y)[/tex] so what you have is not correct.


Your first step should be

[tex]\ln (35- x ^3) = 3 \ln (5-x)[/tex]

Can you proceed from there?
 
i got it thank you...
 

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