Natural Logarithm

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15
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upload_2015-8-31_15-9-38.png

are they equal?
 

BvU

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The first is hard to recognize, but I would take them both as the fourth power of the natural logarithm of (x+3).

The fact they use ln instead of log is decisive.

The first notation is to be avoided: there are already two notations for the base of a logarithm: ##^e\log y## and ##\log_e y## for ##\ln y## and this looks too much like a third notation for the same, which it is NOT.
 
15
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when i tried it on symbolab.com i subtract them both and i'd come up with answer of 0

does that mean they are equal?
 

BvU

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I don't acknowledge that kind of authority in a website. But yes, they are equal for the reason that they describe one and the same thing: the fourth power of the natural logarithm of (x+3).
 
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ok, thank you very much
 
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The first notation is to be avoided: there are already two notations for the base of a logarithm: ##^e\log y## and ##\log_e y## for ##\ln y## and this looks too much like a third notation for the same, which it is NOT.
Just for the record, I have never seen this notation -- ##^e\log y##. By "never" I mean in the past 55+ years. That's not to say that someone hasn't used it somewhere, but if so, it's certainly not in common usage. The notation ##\log_e y## is rarely used, since ##\ln y## is defined to mean log, base e, of y.

If someone were to write ##\log^4 (x + 3)##, I would interpret this to mean the same as ##(\log(x + 3))^4## following the usual shorthand as used in powers of trig functions. I would also interpret the log base to be 10, but in some contexts the implied log base could be e or possibly 2, in computer science textbooks.
 

BvU

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Just for the record, I have never seen this notation -- ##^e\log y##. By "never" I mean in the past 55+ years. That's not to say that someone hasn't used it somewhere, but if so, it's certainly not in common usage. The notation ##\log_e y## is rarely used, since ##\ln y## is defined to mean log, base e, of y.

If someone were to write ##\log^4 (x + 3)##, I would interpret this to mean the same as ##(\log(x + 3))^4## following the usual shorthand as used in powers of trig functions. I would also interpret the log base to be 10, but in some contexts the implied log base could be e or possibly 2, in computer science textbooks.
I now miss how you DO write ##^4\log 16 = 2## ? With the rarely used notation ?

Writing ##^4\log 16## is pretty common in Europe...

Ah, wait, of course ##
^e\log y ## is rarely used because ##\ln y## exists. In fact ##
\log y =\ ^e\log y\ ## for a lot of decent people (mathematicians, for one) :smile: !
 

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