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Wow, stumped. That's amazing... I need to study more.

Hey! I believe I have solved it. I calculated the expected values at the first three consecutive days, and derived a sequence formula for the nth expected value. Then I set it equal to 1,000,000 and voila! I got around n≈117.29 which rounds up to 118 days. Confirmation or flat-out rejection of...

Given the left page scenario, what is the minimum number of days until the expected value rebalances to $1,000,000? The diagram on the right demonstrates pictorially how expected values are calculated per day iteration

Or do you leave out the equals sign altogether when testing intervals?

Okay thank you! :) Last question, let's say the absolute value equation is |x-8|-|x-2|+|x|=6. Then what would the intervals you are testing be? Would it be x<0 , 0<x<2 , 2<x<8 , 8<x ??? or would it be x<0 , 0≤x≤2 , 2<x<8 , 8≤x or would it be x≤0 , 0<x<2 , 2≤x≤8 , 8<x or would it be x<0 , 0≤x<2...

So when dealing with multiple absolute value equations, extraneous solutions are bound to come out? That is, if the solutions are out of the "domain" of the specific boundaries you are testing?

|x-3| + |x+2| - |x-4| = 3 The solution is -6 and 2. What is the method of finding the x? Split into piecewise? If so, how would one split it into piecewise function?

I apologize for the ambiguity. Thank you!

I don't really understand :( I know the answer is 1 but I cannot find what substitution or method to use

I cannot change the bases into a common base for the life of me. Can someone give a suggestion as to how I can proceed in this problem?

Yay it worked! Thank you very much :) Question regarding this method. If -x can be substituted as u, then 3 log_10(x^2) can be written as: 3 log_10(-u^2) ---> 3 log_10(u^2) ---> 6 log_10(u) ? but on the first step, if I move the exponent down earlier, then 3 log_10(-u^2) ---> 6 log_10(-u)...

What happens to the first term when you substitute u = -x? Does the 3 log_10(x^2) ---> 3 log_10((-u)^2) ---> 3 log_10(u^2) ?

Also, when dealing with logarithms, is checking for extraneous solutions essential? What constitutes that a certain logarithmic equation will not yield extraneous solution? Or is it pure arbitrary?

3 log_10(x^2)-log_10^2(-x) = 9 Not really sure how to deal with the log(-x). What can I do with this equation?

Thank you very much!!!

5 * x^[log3(2)] + 2^[log3(x)] = 24

I too learned about the usage of correct terminology. But I only opened up the thread...and mistitled the description at that. So you should thank the others! :)

I have attached a copy of some of the other questions at hand. It's a little messy, as I have taken each question from different worksheets and combined them into one page. I will now copy the directions onto this post exactly as stated on the questions' respective worksheets. #1. Solve for x...

Thank you very much! :) I will elaborate on my background information. I am currently a high school student to be in the senior class this coming school year. I have taken first year differential calculus and am aware of the Newton-Raphson method (in my school we call simply refer to it as...

I apologize for jumping to conclusions about your requests for clarification, as I assumed it was in a belittling manner. The worksheet in which I transcribed the question from merely stated "Solve the following equations", and so I was unable to come up with a valid background of the exercise...