2018年4月27日 · 2 ln(x) is asking e to the power of what is x In this case, e to the power of 2 is e^2 thus, ln(e^2)=2 Another way is using the property of logarithms that says ln(a^b)=b*ln(a) In this case, a=e and b=2 Thus, ln(e^2)=2*ln(e)=2*1=2

Question 579546: The expression ln (2e^3x) is equal to? a. ln 2+3x b. ln(2+3x) c. ln 6x d. ln 2+3

2016年7月31日 · What is a solution to the differential equation #dy/dx=2e^(x-y)# with the initial condition #y(1)=ln(2e+1)#? Calculus Applications of Definite Integrals Solving Separable Differential Equations 1 Answer

2016年8月25日 · ln e^(2x) = 2x As a Real valued function, x |-> e^x is one to one from (-oo, oo) onto (0, oo). As a result, for any y in (0, oo) there is a unique Real value ln y such that e^(ln y) = y. This is the definition of the Real natural logarithm. If t in (-oo, oo) then y = e^t in (0, oo) and from the above definition: e^(ln(e^t)) = e^t Since x |-> e^x …

2017年5月2日 · dy/dx = (2e^(ln^2x)lnx)/x => y'(e) = 2 We have: y = e^(ln^2x) Take Natural Logarithms of both sides: ln y = (lnx)^2 Differentiate Implicitly, and apply the chain rule: 1/y * dy/dx = 2(lnx)*(1/x) Which we can rearrange to get: dy/dx = (2ylnx)/x " " = (2e^(ln^2x)lnx)/x So then, when x=e we have: dy/dx = (2e^(ln^2e)lne)/e " " = (2e^1*1)/e " " = 2

2016年1月1日 · Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e. 1 Answer . Guilherme N.

2016年9月25日 · (x+2)/x This can be significantly simplified first using logarithm rules. The first we will use is that log(AB)=log(A)+log(B), so: y=ln(x^2e^x)=ln(x^2)+ln(e^x) Since ln(x)=log_e(x) and e^x, are inverse functions, we see that ln(e^x)=x. Furthermore, we will also use log(A^B)=Blog(A) for ln(x^2): y=2ln(x)+x Now, to differentiate this, we must know that d/dxln(x)=1/x. Thus: dy/dx=2/x+1=(x+2)/x

2016年1月3日 · What are the first and second derivatives of #f(x)=ln(-2e^(-6x^3)+x^2) #? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer

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2018年2月20日 · x=ln(2)/2 2 e^(2x)=4 e^(2x)=2 Put the natural log function around both sides: ln( e^(2x))=ln(2) Recall the exponential logarithm property which states that log( a^x)=xlog(a) and apply it here: 2xln(e)=ln(2) ln(e)=1 , this is from the basic definition of the natural log function. ln(e)= log_e e=1 since e^1=e.