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Im learning logs right now and Im a bit confused on one of the identies.

 

Can you please clarify this?

 

\(\log_c b = \frac{\log_a b}{\log_a c}\)

 

What is a?
Is it anything we want, is it 10?

 

Thanks

 Dec 26, 2020
 #1
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Yes, it can be anything.

 Dec 26, 2020
 #2
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I think this is often referred to as the base change identity

 

logb =   x       means     cx = b

 

cx=b                           now take loga of both sides

x loga c = loga b         now divide both sides by loga c

x =  loga b / loga c      see that red equation above?   x = logc b   ....sub that in for x

 

logc b  = loga b / loga c     which is your identity !

 Dec 26, 2020
 #3
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Excellent, Guest   !!!!

 

 

cool cool cool

CPhill  Dec 27, 2020

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