What Connects the Natural Logarithm of i with Pi? - Physics Forums
2011年1月31日 · Why does ln(i) = (1/2pi)i? I was bored the other day and wondered whether or not it would be possible to find out the natural log of the imaginary number i. Typed it into my TI-84 and it said the answer was 1.57079632i. I wondered why the might be the case, thought about it for a while and...
How Do You Prove This Integral Equals \(\frac{\pi}{2}\ln \pi\)?
2013年10月21日 · Thanks again to those who participated in last week's POTW! Here's this week's problem! ----- Problem: Show that $\displaystyle \int_0^{\infty}...
Find the limit of ln (sinx) as x approaches pi - Physics Forums
2013年1月27日 · Ln (sinx) as x approaches pi-, that is, as x approaches pi from the left. I thought I should use the squeeze theorem, but I am not sure how to apply it. My teacher is not requiring us to use the delta/Epsilon method, so I am sure it is a squeeze method. But how do I set it up? I tried -1 < sinx < 1, Thus ln (-1) < ln (sinx) < ln (1)
How do I solve the equation e^(x+3) = pi^x? - Physics Forums
2003年4月4日 · Yeah, you're kinda butchering things with your "ln raised to a power" and "ln by itself" stuff. Step 1. Take the natural logarithm of both sides of the equation: ln(e^(x+3)) = ln(pi^x) this becomes x+3 = x * ln(pi) Step 2. Isolate x on one side of the equation 3 = x * ln(pi) - x 3 = x (ln(pi) - 1) Step 3. Solve for x x = 3 / (ln(pi) - 1) - Warren
Interpret Riemann sum to determine integral - Physics Forums
2024年12月1日 · ln(pi/4 + x^2) as the (i pi/2n) term is the 'x' term. How do I determine the limits of the integral, however? I was thinking about using the lower bound of the summation --> this given the (pi / 2n)^2 term, implying that nothing was 'added' as the 'left' side bound. So I conclude that the lower limit, which we'll call a = 0
Can You Prove ln(e)/e > ln(pi)/pi Without Calculations? - Physics …
2005年4月10日 · Well, since you can prove that ln(e)/e is the maximum value for f, we also have: [tex]\pi(ln(e))>eln(\pi)\to{ln}(e^{\pi})>ln(\pi^{e})[/tex]
Integral of ln(1+tanx) from 0 to pi/4 | Homework Equations
2012年8月10日 · Homework Statement Evaluate the following integral: Homework Equations \int_{0}^{\frac{\pi }{4}}ln(1+tanx)dx The Attempt at a Solution I tried to... Insights Blog -- Browse All Articles -- Physics Articles Physics Tutorials Physics Guides Physics FAQ Math Articles Math Tutorials Math Guides Math FAQ Education Articles Education Guides Bio/Chem ...
Solving Ln(-1) with Euler's Equation - Physics Forums
2005年3月22日 · ok don't kill me, hear me out before you say its undefined: e ^ { \pi i}= -1 so taking the natural log of both sides yields: ln(-1) = \pi i... Insights Blog -- Browse All Articles -- Physics Articles Physics Tutorials Physics Guides Physics FAQ Math Articles Math Tutorials Math Guides Math FAQ Education Articles Education Guides Bio/Chem ...
Solve Integral of ln(sin x) from 0 to pi. - Physics Forums
2014年12月15日 · Evaluate the integral \int_{0}^{\pi} \ln (\sin x)\,dx. Remember to read the...
Wolfram Alpha graph of ln(x) shows as ln(abs(x)) - Physics Forums
2017年10月14日 · Ln is well defined for negative numbers then, which shows up as having an imaginary part of pi (for the principle branch). It just looks like the ln of an absolute value, which happens to be the real part. For the principle branch we have: $$\ln(-x)=\ln(e^{\pi i}\cdot x)=\pi i …