Solving Logarithmic Equations for Homework Help

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The discussion revolves around solving the logarithmic equation log(49/4) + log(9/35) - log(21/10) and whether it equals log(2/3). Participants emphasize the importance of using logarithmic properties, such as log(a) + log(b) = log(ab) and log(a) - log(b) = log(a/b). There is confusion about notation, particularly regarding whether log(1/5) is correctly interpreted. The community encourages clarity in expressions and suggests re-evaluating the calculations. The overall goal is to find the correct simplification and solution to the logarithmic equation.
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Is log49/4+log9/35-log21/10 = log2/3 ?

I've tried and I'm here 2log1/5+2log2/5-log7=log2/4 , if I didn't do anything wrong, but I don't know what to do then , please help me !
 
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log(a) + log(b) = log(ab) is one of the useful properties of logarithms
 


enibaraliu said:
Is log49/4+log9/35-log21/10 = log2/3 ?

I've tried and I'm here 2log1/5+2log2/5-log7=log2/4 , if I didn't do anything wrong, but I don't know what to do then , please help me !
Please use parentheses! Does "log1/5" mean log(1/5) or log(1))/5? And please show how you got that result.
 
Hi enibaraliu! :smile:
enibaraliu said:
Is log49/4+log9/35-log21/10 = log2/3 ?

I've tried and I'm here 2log1/5+2log2/5-log7=log2/4 , if I didn't do anything wrong, but I don't know what to do then , please help me !

erm :redface: … log A + log B = log AB

log A - log B = log A/B

Try again! :smile:
 

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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