logaritm & In?

Question

watz? In................
watz? da relation betn log and In........................
if y=In x; dy/dx=1/x (is it correct or wrong).....................(1)
or
if y=log x;dy/dx=1/x(is this correct or wrong).............................(2)
In some books the first one is given
while in other da second one.
which is right among da 2.

Answer 1

The use of "log" to mean base 10 is becoming outdated.
If a book says y=logx and dy/dx = 1/x then it means log
is the natural log. Paritosh is wrong in saying that the
antiderivative is the same no matter what base you use
as follows.

y=lnx
dy/dx = 1/x

if y=logx means base 10, you must convert to ln like this
10^y=x
yln10 = ln x
y = lnx/ln10
dy/dx = 1/(xln10)

Answer 2

This is just a difference of notation. Some books write "ln" to mean natural logarithm, and some books write "log" to mean natural logarithm. Both mean the base e logarithm.

Some people (and a few books) write "log" to mean the base-10 logarithm.

The derivative of the base-10 logarithm is computed as follows:
y = log10 (x)
y = ln (x) / ln (10)
y' = 1/(x ln 10)

Answer 3

You can take a logarithm with different base numbers.
integral ( 1/x ) = log_e |x| = ln |x|

Typically you have:
log = log_10 (in some books log = ln)
ln = log_e (also called the natural logarithm)

But you can also have:
log_2 (important is computer science)

Generally you can convert any logarithm into another one with this formula:

log_a x = log_b x / log_b a

So you can calculate any logarithm on your calculator, for example:

log_2 128 = log 128 / log 2 = 7
because 2^7 = 128

The rules for calculating with logs is the same for all bases.

Answer 4

In advanced mathematics log is the multivalued version of the function ln, which is itself the logarithm to the base e, where e is exp(1).
However log when given with a subscripted quantity means the logarithms is that to the base of the given quantity. However this may be confusing as the nested logarithm log log log .....log z
can also be given similarly.

Answer 5

ln is just a specific case of log, namely log in base e.

log may be in any base, although in some books base e is implied in which case log = ln. At other times base 10 is implied. For clarity, it's always best to explicitly say what the base is.

if y=In x; dy/dx=1/x ---> always correct
if y=log x;dy/dx=1/x ---> only if the base is e. If the base is b, then

y=logx ---> y=lnx/lnb ---> dy/dx = 1/(x*lnb).

Answer 6

The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e, where e is equal to 2.718281828459... (continuing infinitely).

and

The logarithm(log) is the mathematical operation that is the inverse of exponentiation (raising a constant, the base, to a power). here log means natural logarithm if no base is specified. This is the reason why it is confusing.

if y=In x; dy/dx=1/x its perfectly ok.

Because, the logarithm is natural.

And it is correct both ways, since the antilog would exist no matter what base you take with logarithm.



I hope that it is clear now.

All the best.

Answer 7

logarithm to the base e is called as ln.
the relation between ln and log is
ln=2.303log.
and as far as i've read both the first and second equations r correct
ok..
bye

Answer 8

ln is the logarithm to base e.
ln = 2.303log (base 10)
d(ln x)/dx = 1/x it is correct


this one is also correct