What is the difference between log and ln? I was told that its

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What is the difference between log and ln?  I was told that its

David Clayton · Accepted Answer

Usually log⁡(x) means the base 10 logarithm; it can, also be written as log10(x).    log10(x) tells you what power you must raise 10 to obtain the number x.    10x is its inverse.    ln⁡(x) means the base e logarithm; it can, also be written as loge(x)    ln⁡(x) tells you what power you must raise e to obtain the number x.  ex is its inverse.

chumants6g · Accepted Answer

ln⁡  is always  log⁡e , the logarithm base  e .  When you specify the base you should always use  log⁡b , ln⁡b  doesn’t make sense.  When  log⁡  is used without an explicit base, it’s usually one of the following options:  The base is  e ,  At some previous point, the author explicitly set that “all logs should be understood as base b”,  From the context, the base, if not  e , is clear - and it will usually be 2, or, less often, 10.  It doesn’t matter. For instance, if the statement is that a function is  O(log⁡n) ,it’s an equivalent statement to say it’s  O(logbn)  for any base  b , since the different log functions are just the same function scaled by a constant, i.e.  loga(x)=Clogb(x)  for a constant  C  that only depends on  a  and  b  (but not  x ).

Vasquez · Accepted Answer

Yes, big difference.
Log is used for base ten. You’ve probably seen an equation like this:
$10^{x} = y$ , where y is equal to 10 raised to the power x.
If you know y how do you find x?
You take the Log of the equation $10^{x} = y$
$\log (10^{x}) = \log y$
$\log (10^{x}) = x$
So
$x = \log y$
Ln is the natural log. The natural log is used to solve for a when you know b in the following equation:
$e^{a} = b$ , where e is approximately 2.718, this is the natural exponential.
to solve for a when you know y, take the natural log of $(e^{a} = b)$
$\ln (e^{a}) = \ln b$
$\ln (e^{a}) = a$
So
$a = \ln b$
So how does Ln y compare to $\log y$
Let $y = 10^{c} = e^{d}$
$\log y = c and \ln y = d$
$10 = e^{2} .3026$
Then $y = 10^{c} = (e^{2.3026})^{c} = e^{[} 2.3026 c]$
$y = e^{d} = e^{[} 2.3026 c]$
$d = 2.3026 c$
$\ln (y) = 2.3026 [\log (y)]$
$\log (y) = 0.4343 [\ln (y)]$
Hope this helps

What is the difference between log and ln? I was told th

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