Proofs: Logarithm - Clues for Understanding

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    Logarithm Proofs
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The discussion revolves around understanding logarithmic equations and the need for clarity in problem statements. Participants express frustration over vague requests for help without specific problems outlined. The first equation, "loga xy = y loga x," is identified as needing proof rather than just acceptance. The second equation, involving trigonometric functions, also requires proof, which some participants struggle with. Overall, the conversation emphasizes the importance of clearly defining problems to facilitate effective assistance.
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Got no clue .. need some clues
 

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ok i figured out 1.. bu still no clue as to .2 !
 
How can you expect people to help you if you don't tell them what the problem is?

In your pdf attachment (7) says "loga xy= y loga x". That is an equation, not a "problem". What are you to do with the that equation?

(2) says "x\in [-1, 1] cos(arcsin x)= sin(arccos x)&quot;<br /> Again, that is an equation. What are you to do with it.
 
I had to prove the equation, but I figured it out.

Same for 2, I need to prove the equation and not just asume that it exists!
That one I couldn't prove..
 
Number 1 was just the power rule. Number 2 I don't know either sorry.
 
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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