Log in Joey Jang 7 years agoPosted 7 years ago. Direct link to Joey Jang's post “How did a mathematician f...” How did a mathematician find e? What's its origin? • (22 votes) Divy Shah 4 years agoPosted 4 years ago. Direct link to Divy Shah's post “It is often called Euler'...” It is often called Euler's number after Leonhard Euler (pronounced "Oiler") e is the base of the Natural Logarithms (invented by John Napier). e is found in many interesting areas, so is worth learning about. you can check this link to find out: (12 votes) Matthew Johnson 7 years agoPosted 7 years ago. Direct link to Matthew Johnson's post “in `log_1(1)=x`, doesn't ...” in • (9 votes) Kim Seidel 7 years agoPosted 7 years ago. Direct link to Kim Seidel's post “See the "Restrictions" se...” See the "Restrictions" section at this link (about 1/2 down page). The base is restricted from being 1. (18 votes) svlohit2012 4 years agoPosted 4 years ago. Direct link to svlohit2012's post “Why would you need to use...” Why would you need to use ln? • (9 votes) SherlockHolmes.42 4 years agoPosted 4 years ago. Direct link to SherlockHolmes.42's post “The natural log function,...” The natural log function, ln, is the log with a base of Euler's number, e. Here is an example of when it can be used: This is the most common way I've seen the natural log used, but there are no doubt other ways to use it. (9 votes) Haoyu Wang 2 years agoPosted 2 years ago. Direct link to Haoyu Wang's post “why e^𝝿i+1=0?How did Eu...” why e^𝝿i+1=0? • (8 votes) KLaudano 2 years agoPosted 2 years ago. Direct link to KLaudano's post “It is a specific case of ...” It is a specific case of his formula, e^(i*x) = cos(x) + i*sin(x). The proof of this formula requires Calculus level math though (e.g. power series or differentiation). brandon_bolster 5 years agoPosted 5 years ago. Direct link to brandon_bolster's post “Is ln the same thing as l...” Is ln the same thing as log base 10? • (7 votes) Oliver 5 years agoPosted 5 years ago. Direct link to Oliver's post “The "log" key on a calcul...” The "log" key on a calculator is log base 10. "ln" is natural logarithm, and there is a video for that here: https://www.khanacademy.org/math/algebra2/exponential-and-logarithmic-functions/e-and-the-natural-logarithm/v/natural-logarithm-with-a-calculator (7 votes) Sellov 4 years agoPosted 4 years ago. Direct link to Sellov's post “What is log_15 (9), if lo...” What is log_15 (9), if log_15 (5) = a Could someone explain the steps to solve this? • (7 votes) Katriana 2 years agoPosted 2 years ago. Direct link to Katriana's post “I can explain how to chec...” I can explain how to check it, at least, though I'm not sure that this is how you would originally come to this answer. (5 votes) Andy Huang 6 years agoPosted 6 years ago. Direct link to Andy Huang's post “How do you do log base 2 ...” How do you do log base 2 x + log base 3 x = 4? • (6 votes) Muhammadaminbek 7 years agoPosted 7 years ago. Direct link to Muhammadaminbek's post “Can anyone explain to me ...” Can anyone explain to me how to solve e^ln^2 x +x^lnx =2e^4 • (5 votes) Matthew Johnson 7 years agoPosted 7 years ago. Direct link to Matthew Johnson's post “Why is the base 10 logari...” Why is the base 10 logarithmic scale the standard for calculators? • (1 vote) Judith Gibson 7 years agoPosted 7 years ago. Direct link to Judith Gibson's post “Probably because the rest...” Probably because the rest of our number system is built around powers of 10 --- tens, hundreds, thousands, etc. and tenths, hundredths, thousandths, etc. (7 votes) Julicz 3 years agoPosted 3 years ago. Direct link to Julicz's post “e is the base of the Natu...” e is the base of the Natural Logarithms (invented by John Napier), how did he did it and did he calculated the logarithms by hand? • (3 votes)Want to join the conversation?
e is an irrational number (it cannot be written as a simple fraction).
https://www.khanacademy.org/math/in-in-grade-11-ncert/in-in-exponential-and-logarithmic-functions/copy-of-math3-e-and-natural-log/v/e-through-compound-interest and https://www.khanacademy.org/math/in-in-grade-11-ncert/in-in-exponential-and-logarithmic-functions/copy-of-math3-e-and-natural-log/v/e-as-limitlog_1(1)=x, doesn't x = infinity?
https://www.khanacademy.org/math/algebra2/exponential-and-logarithmic-functions/introduction-to-logarithms/a/intro-to-logarithms
e^x = 2
--> To solve for x, we would take the ln of both sides. This is because x is the exponent of e, and the e and natural log will cancel out when put together.
ln(e^x) = ln(2)
x = ln(2)
How did Euler proof this equation?
The answer is: 2-2a
log_15(5)=a, and we want to see whether log_15(9)=2-2a. We can begin by finding a.
log_15(5)=a
log(5)/log(15)=a Use the change of base rule.
a=approx. 0.5943
Next we can find 2-2a:
2-2*approx.0.5943 Try to use the entire answer you got for a, instead of a rounded one, if you can.
2-approx. 1.1886=approx. 0.8114
Now we can find log_15(9), and see if it equals 0.8114.
log_15(9)=log(9)/log(15) Change of base rule.
log(9)/log(15)=approx. 0.8114
log_15(9)=2-2a True.
This shows that it is indeed the case that if log_15(5)=a, then log_15(9)=2-2a, but it does not seem like it is the way that you would come to figure it in the first place.
Perhaps if you figured that a=approx. 0.5943, and that log_15(9)=approx. 0.8114, you might just happen to notice that 0.8114+2(0.5943)=approx. 2. I have not figured anything better than this for this question. Maybe someone else will. For now, I hope you have a good day. Keep going!
