Natural Log; It's a logarithm with a base of e, a natural constant.
You can also write this as ln(6 times 4)
Do you mean this symbol ∈ (or backwards 3) if so, it means is an element of; Also, ∉ (with strikethrough) (or backwards 3 with strikethrough) is the symbol for "is not an element of" used in set membership. See also Element (mathematics) and Set (mathematics)
I don't believe that the answer is ln(x)x^(ln(x)-2), since the power rule doesn't apply when you have the variable in the exponent. Do the following instead:y x^ln(x)Taking the natural log of both sides:ln(y)ln(x) * ln(x)ln(y) ln(x)^2Take the derivative of both sides, using the chain rule:1/y * y' 2 ln(x) / xy' 2 ln(x)/ x * yFinally, substitute in the first equation, y x^ln(x):y' 2 ln(x) / x * x^ln(x)y'2 ln(x) * x ^ (ln(x) - 1)Sorry if everything is formatted really badly, this is my first post on answers.com.
int(ln(x2)dx)=xln|x2|-2x int(ln2(x)dx)=x[(ln|x|-2)ln|x|+2]
The derivative of e^u(x) with respect to x: [du/dx]*[e^u(x)]For a general exponential: b^x, can be rewritten as b^x = e^(x*ln(b))So derivative of b^x = derivative of e^u(x), where u(x) = x*ln(b).Derivative of x*ln(b) = ln(b). {remember b is just a constant, so ln(b) is a constant}So derivative of b^x = ln(b)*e^(x*ln(b))= ln(b) * b^x(from above)
It depends. If you mean (ln e)7, then the answer is 1, since (ln e) = 1. If you mean ln(e7), then the answer is 7, since ln(e7) = 7 (ln e) and (ln e) = 1.
in math, ln means natural log, or loge and e means 2.718281828
In elementary mathematics, any subset of R+, the non-negative real numbers.
Do you mean ln(x-2), or ln(x)-2? If it is ln(x-2): 1/(x-2) If it is ln(x)-2: 1/x
long neck
Lactating nurse
if x8 = 20 then x = - eighth root of 20 or x = eighth root of 20 eighth root of 20 = 1.4542154.... Maybe you mean 8x = 20 If so Ln (8x) = Ln (20) => x Ln(8)= Ln(20) => x = Ln(20)/Ln(8) = 1.4406426...
Assuming you mean 'logarithm to the base 'e' ( natural logarithm. On the calculator its symbol is 'ln'. Hence ;ln 2 = 0.69314718....
The LN button on a graphing calculator represents the natural logarithm function, which is the logarithm to the base e, where e is approximately equal to 2.71828. It is commonly used in mathematics, particularly in calculus and exponential growth problems, to solve equations involving exponential functions. The natural logarithm has useful properties, such as converting multiplication into addition, which can simplify complex calculations.
The order of operations is not quite clear here.If you mean (ln 2) + x, the derivate is 0 + 1 = 1.If you mean ln(2+x), by the chain rule, you get (1/x) times (0+1) = 1/x.
Ln 4 + 3Ln x = 5Ln 2 Ln 4 + Ln x3= Ln 25 = Ln 32 Ln x3= Ln 32 - Ln 4 = Ln (32/4) = Ln 8= Ln 2
it means changing the mathematics information