Help with math

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>>358967
easily

>>358974

If you replace P with 45 you would get y^45 + 1 = y^15, which isn't equal

>>358976
If y> = 3 then the equation is true

>>358976
And if y = 0 or y<= -3 is also true

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>>358978

My calculator says they're equal, but WolframAlpha says it's not. It probably has something to do with the number being too big though.

>>358967
You have to take the log of both sides Brother.

>>359055
but then you get log(y^45 + 1), not log(y^45) + log(1)

>>359070
by the way that alone should tell you how to solve it
log-base-y of both sides

guess how you find out the log of something in a certain base?
hint, division is involved
you should be able to figure this one out

>>359070
you're right. that's the log of a sum, which you would usually leave alone -_-
if you either look at the graph of log_y(y^45+1) = P or test different values of y to find P, you'll find that P varies with y; there is no one value for P
P= log_y(y^45+1)
hm. I guess you could use a Taylor series to approximate P.
WolframAlpha gives a useful-looking result: the expansion about x = inf is
45 + 1/(x^45 lnx) + O((1/x)^79)
I THINK that order is small enough such that you can ignore it and reasonably say, but I'm not sure if that what it signifies
P ≈ 45 + 1/(x^45 lnx)

anons pls correct me I didn't learn this

>>359193
you don't need to be really complicated
http://home.windstream.net/okrebs/page57.html
it's done in very few steps as possible and you've solved for P

P is 45, but not really. With an exponent of 6 or something, it's clear that P is something slightly higher than 6. But when you have 45, that difference is so freaking small that Wolfram will tell you P=45 for any y. Ask for more digits, and you'll find them after dozens of 0s. Not sure what to write down for the teacher, but that's what's going on.

this stupid crap right here is why people hate math

>>359267
just because some roodypoos tell OP to consider sum of logs instead of log of sum doesn't mean math is bad

>>359298
I think he's saying that it sucks because of counter-intuitive things like this. On the surface, it makes no sense that (thing) + 1 = (thing), just like .99999 = 1 or infinity - infinity being undefined (it's obviously 0 - NOT). But that's how things work out, and people can prove these things in various ways.

i don't get why you guys are trying to figure out the numerical value of P
that's not what it's asking at all
it's just asking to solve for P
what the actual numbers are is irrelevant
you won't come to a conclusion that quickly especially with y still in play

>>359264

If P isn't 45, then there would be no other answer, so I'll just take it as that

>>359397
i just literally explained the post above you einstein

>>359405
So p= (log(y^45 +1) +2 pi n)/ log(y) ?

>>359407
huh? where did the 2pi n come from?

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>>359408
thats what wolframalpha gave me

>>359413
must be some identity thing i forgot? i don't know about that answer
all you really need to do is take log (base y) from both sides and the right side (y^P) is just P as a result but the left side is logy(y^45+1)/log(y) as per rule of base conversion
it was a simple one step problem and that's your answer for P, what the numeric values are at this point are not relevant as long as the denominator doesn't create a NAN like division by zero or something

>>359414
>logy(y^45+1)/log(y)
whoops, just meant log for that first thing

>>359413
>>359414
>>359415
and finally [spoiler]sorry i'm playing vidya right now[/spoiler] the inequalities they give are kinda relevant for the stated above reason of NAN since you can't have log(x) where x <= 0?
don't pay attention to the 45 thing and that reply wasn't even done right to begin with because that is not a logarithmic identity

>>359417
got it, thanks anon

>>359418
you are welcome
now help me find the name of this song >>359073