Understanding Logarithmic Function Problems: Solving for x

AI Thread Summary
To solve the equation Log(35-x^3)/Log(5-x)=3, the logarithmic properties can be applied, specifically Log(a/b)=Log a - Log b. By moving Log(5-x) to the right side and eliminating the logarithms, the problem simplifies to an algebraic equation. Initial attempts suggested potential solutions of 3 or 2, but further calculations indicated a different value around 0.289. Ultimately, the key to solving this problem lies in proper manipulation of the logarithmic expressions and subsequent algebraic simplification.
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Homework Statement


solve x.
Log(35-x^3)/Log(5-x)=3


Homework Equations


Log(a/b)=Log a - Log b


The Attempt at a Solution


The answers would be 3 or 2
(so I'm guessing it has sumthing to do with quadratics)
i tried to expand the left side first, then rearrange it to Log(7/x^4)=3
the problem is that's not giving me the answer, which i got was 0.28925076.
 
Last edited:
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The relevant equations you gave aren't necessary for the problem.
Move the Log(5-x) to the right hand side, then eliminate the logarithms. Then its just an algebra problem.
 
Thanks.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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