Properties of Logarithms, Division and Multiplication

AI Thread Summary
The discussion focuses on expressing the logarithmic expression loga(x8w/y2z4) in terms of logarithms of x, y, z, or w. Participants reference key logarithmic properties, specifically the quotient and product rules. An initial attempt at solving the problem reveals a common mistake of not properly handling exponents. The realization of this error leads to a corrected approach in the solution process. The conversation emphasizes the importance of accurately applying logarithmic properties when simplifying expressions.
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Homework Statement


Express in terms of logarithms x, y, z or w.

Problem:

loga(x8w/y2z4)


Homework Equations



log(u/w) = log u - log w
log(uw) = log u + log w

The Attempt at a Solution



Here are my attempts:

owyu2.png


As you can see, the answers are pretty similar. I'm assuming I made a small syntactical mistake.
 
Last edited:
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Nevermind... realized that I didn't bring the exponents out front.
 

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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