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.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
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Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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