The square bracket means include the endpoint. It seems I am assuming too much. If it doesn't say strictly, I concede the argument.
Thank you for everything!!!!!!! bob bundy!!!!!! plus congrats to owner..admins..moderators etc. for this great site! cheers!
They are the same because
But the book shouldn't be saying less than and equal to because the graph has a turning point when = so dy/dx = 0
So the value of the function isn't getting bigger.
wow! they are the same indeed! I feel sooooo much better now!
Well, the book says (-infinity, -1/2*ln3] , so I guess it includes -1/2*ln3 probably because the question doesn't ask where the fuction strictly...increases..that must be it! right?
OK, here we go.
Your differentiation is correct. For an increasing function you want dy/dx to be > 0
e^x is always positive so you need
log base e is an increasing function so the inequality holds if you take logs
Your approach seems wonderful!!! and according to me correct.. but why does the book i have give another..but very similar answer?.. it says x<or=-1/2*ln3 Is it the same but i'm missing smth??
Hi Bobbym! I don't think i have to find a rational number. Usually the answer to these logarithmic problems is smth like x=ln3/ln5 .To answer your great questions:
1)It comes from the book called Essential Mathematics for Economic Analysis 4th edition on page 123 problem 3.(a)
2)I am mostly interested in the logical thinking process in these kind of problems.
Hello all! I am new here and I am a student having a hard time in math. I have the following natural logarithms problem and it is giving a hard time. Can someone please help with the solution? And also if possible evaluate the difficulty of this problem?
Solve for x: 4^x-4^(x-1)=3^(x+1)-3^x