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

Thread starter thomasrules
Start date Feb 22, 2005

AI Thread Summary

The equation log(35-x^3)/log(5-x)=3 simplifies to 1000=(35-x^3)/(5-x) through the property of logarithms. By rewriting the logarithmic equation, it becomes clear that taking the anti-log leads to the relationship between the two expressions. The correct first step involves expressing the logarithmic equation in terms of natural logarithms, specifically ln(35-x^3) = 3 ln(5-x). This transformation allows for further simplification and solving of the equation. The discussion concludes with the participant confirming their understanding of the simplification process.

Feb 22, 2005

thomasrules

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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Feb 22, 2005

Jameson

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MHB

Putting this in a better grouping you get 3log(5-x)=log(35-x^{3})

Take the anti-log of both sides from there.

Last edited by a moderator: Feb 22, 2005

Feb 22, 2005

Integral

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\frac {\ln x} {\ln y} \neq \ln ( \frac x y) so what you have is not correct.

Your first step should be

\ln (35- x ^3) = 3 \ln (5-x)

Can you proceed from there?

Feb 22, 2005

thomasrules

i got it thank you...

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