# If I differentiate log x, do I get 1/x ?Watch

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#1
I was told so, but I don't quite get why.

because the differential of ln x = 1/x

and obviously log x is not the same as ln x
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5 years ago
#2
(Original post by Jack93o)
I was told so, but I don't quite get why.

because the differential of ln x = 1/x

and obviously log x is not the same as ln x
It depends what base you are using. If that is log to base e (it is quite common for log to mean this rather than base 10 and so on) then yes. If it isn't then no.
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5 years ago
#3

1
5 years ago
#4
one way to see this is by putting: then

then, take dx/dy - not dy/dx:

so then, taking the reciprocal:

(not very rigorous, but hopefully easy to follow)
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5 years ago
#5
Another proof in Spoiler
Spoiler:
Show

sub

let

After sub, derivative is:

sub

let

Derivative becomes

.
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5 years ago
#6
Sorry to interrupt! Please can somebody help!!??? I am probably being really dense but how do you solve 3sinx-4cosx=3 in the range where x is between 0 and 2π??? Thank you ever so much!!
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5 years ago
#7
(Original post by EmilyJones123)
Sorry to interrupt! Please can somebody help!!??? I am probably being really dense but how do you solve 3sinx-4cosx=3 in the range where x is between 0 and 2π??? Thank you ever so much!!

Express 3sin x - 4 cos x in harmonic form (in the form or ).
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