# How do you differentiate log10 x?

with 10 being the base of log, what do i do? i know something about log10 being like ln x or something

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• Anonymous
9 years ago

You know nothing .....:-) or, better, you know wrong.

"log10 being like ln x or something" is senseless.

So, here we go

Let y = log_10 x ---> 10^y = x

Take ln of both sides ----> y ln(10) = ln x

Take d/dx of both sides ---> ln(10) dy/dx = 1/x ----> dy/dx = 1/(x ln (10))

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RE:

How do you differentiate log10 x?

with 10 being the base of log, what do i do? i know something about log10 being like ln x or something

Source(s): differentiate log10 x: https://biturl.im/9FJ5X
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• It's not an answer but a query : whether 10 stands for base or the problem is like y = 2x lox (10* rootx) ? The differentiation will depend on the log base. All the best

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• Anonymous
9 years ago

Go with the previous entry. That should be right and looks pretty decent. However, ln(x) does not represent any base for the function-- like log10 or log 2 or any other base for the log function-- it represents the log base e but can be used basically any log function to convert it to simpler terms. (all of this stuff can be found on most any calculator too) but to differentiate it follow the guy from the previous one.

Source(s): knowledge
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• To convert log(x) to the natural-base logarithm,

log(x) = ln x / ln 10

Considering (1 / ln 10) as a constant value, and using the Multiplication Rule

d/dx (1 / ln 10) ln x

= (1 / ln 10) (1 / x) + (0) (ln x)

= x / ln 10

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• Whatever the base of the log is, 10, 2 whatever.

It's always ln|x|

d/dx(logx) = ln|x|

Make sure absoulte value, critical stuff there

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• y = log(x) = ln(x) / ln(10)

y' = 1/(x ln 10) = log(e) / x

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