Aug 31, 2017 · Since it is many to one, the complex valued logarithm #ln x# that extends the real valued logarithm has multiple branches. The principal logarithm is usually taken to have values …

Jun 1, 2018 · If you mean differentiate w.r.t t, firstly write it as : z(t) = alpha beta^t, qquad {(alpha = 23000),(beta = 0.93):} Then maybe use log rules: ln z = ln alpha + t ln beta Differentiate (?): 1/ …

Dec 10, 2016 · There are 2 real solutions: x ≈ ± 2.63571322227139... The equations cannot be solved by algebraic methods. You can solve the equations: -2sin(x) - ln(-x) = 0; -oo < x < 0 …

Mar 27, 2018 · Converges by the Comparison Test. First, I am going to assume the series does not start at zero, as zero is not in the domain of the sequence. Moreover, ln(0) DNE. Also, the …

Sep 27, 2015 · What is the derivative of #ln((e^x)/(1+e^x))#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 2 Answers

Dec 13, 2015 · Yes, they are. Here is how: #DeltabarS = int_(T_1)^(T_2) (barC_P)/T dT# #DeltabarH = int_(T_1)^(T_2) barC_P dT# ...

Apr 14, 2018 · See below. We must use integration by parts for this problem. We let u = ln|x+ 1| and dv = x. It follows that int u dv= uv - int vdu int ln|x + 1|x dx= 1/2x^2ln|x + 1| - int 1/2x^2(1/(x …

Jul 2, 2017 · See below. Recall that the derivative of e^x is e^x. The function e^x is an exponential function with the irrational Euler's Number as base. Here is why the derivative of e^x is e^x: y …

Dec 7, 2015 · I found: x=0.789 We can write (using the definition of log): 44=121^x then 11*4=11^(2x) taking 11 to the right: 4=11^(2x)/11 using the property of the quotient of …

May 27, 2017 · The integrated rate law for a first-order reaction #"A " -> " products"# looks like this. #color(blue)(ul(color(black)( ln( (["A"]_t)/(["A"]_0)) = - k * t)))#