what is differential of log x & ln x?

Question

d(log x)/ dx & d(ln x)/dx (calculus)

Answer 1

what is differential of log x & ln x?

d(log x)/ dx & d(ln x)/dx (calculus)

log x = log of x to the base 10
ln X = log of x to the base n
d/dx of log x = 1/(x ln10)
d/dx of ln x = 1/ (x ln n)

Answer 2

2

Answer 3

Derivative Of Log Base 10

Answer 4

log just means logarithm, the inverse of an exponent.

logx = a is the same as
10^a = x

The ten comes from the fact that log written by itself is assumed to be in base ten. If it were written log3 x = a (the three being a subscript) then that would be base 3 and 3^a = x would apply.

ln is just the term for the "natural logarithm", which is log base e (Euler's number: 2.71828...). This is given its own notation because in calculus, e and the natural logarithm are extremely important.

Hope this helps.

Answer 5

Ln is the natural logarithm (i.e. to the base e). The derivative of ln(x) is 1/x.

Log is the logarithm base 10, so log(x)=ln(x)/ln(10). THis means that the derivative of log(x) will be 1/[xln(10)].

Answer 6

The answers are correct, but the difference is only a constant multiple:

ln(x) = ln(10)*log(x)

ln(x) = 2.303*log(x)

Answer 7

Okay, a lot of confusing answers there.

Log X = "log to base 10" of X

ln X = 'natureal log' of X

natural log is "log to base e"

Answer 8

Log x =y (say) is nothing but logarithm of x having base 10 i.e. x^y =10.
whereas, Ln x =z (say) is nothing but logarithm of x having base e. That means, x^z=e.
Hope I have explained correctly.

Answer 9

ln x=a is e^a=x (e is the base.)
log x=a is 10^a=x (10 is the base.)
e is:- 1+1/1!+1/2!+1/3!......(have unlimited characters )

Answer 10

ln of x is the log base e of x.
log (without a base specified) is the log base 10 of x

Answer 11

well i know "In x" is the inverse of x, meaning 1/x

log x is a function of x, for example:

The log base x of 5 is written as:

log 5
x