how to solve for x? 3^x x+4

Question

how to solve for x?   3^x > x+4

swissgirl · Answer

well I am a cheater I just graphed the 2 functions

zzr0ck3r · Answer

hehe, still what is the exact point ?

swissgirl · Answer

x>1.5619188

zzr0ck3r · Answer

well first off there will be equal at two points, but I need to know how to do it without calc.

swissgirl · Answer

ya whoops i needed to find the intersection for the other point. I can give it to u butt i dont know how to solve this without a calc. it gets confusing with ln and stuff

zzr0ck3r · Answer

yeah I know the two points, but not exact.

zzr0ck3r · Answer

wolfram does something funny.

swissgirl · Answer

so $ x<-3.987483 \text { and } x>1.5619188 $

zzr0ck3r · Answer

yeh, I dont think this is solvable at our level. http://www.wolframalpha.com/input/?i=solve+3%5Ex+%3E+x%2B4++ check that out

zzr0ck3r · Answer

yeah I dont know the two base functions they use. maybe next year ill try again:)

zzr0ck3r · Answer

tnks for looking and thinking:)

swissgirl · Answer

next yr? what is this for?

zzr0ck3r · Answer

nothing. I am a math major, so im thinking maybe ill learn about those two functions by then.

swissgirl · Answer

I am a math major and dont know a thing :(

zzr0ck3r · Answer

I think the higher we go, the more we dont know.

zzr0ck3r · Answer

what class you in now?

swissgirl · Answer

ummm its more of a advanced discrete math class. Just alot of proving

swissgirl · Answer

ok dumbcow will have the answer lol

zzr0ck3r · Answer

yah im taking descrete in the fall. Was actually helping a girl today in descrete prove that something was one-to-one. (we covered it in some proof writing class)

dumbcow · Answer

yeah, these type of problems can't be solved algebraically
..no i can't do it either, but thats why there is solving analytically with technology :)

dumbcow · Answer

btw i was math major as well and i never was taught the product log function that wolfram uses

swissgirl · Answer

hahah i still feel stupid cant prove a dumb thing

zzr0ck3r · Answer

ahh ty for info.

zzr0ck3r · Answer

what dumb thing?

swissgirl · Answer

i cant prove nething at all. Like I always get stuck at some point or other

zzr0ck3r · Answer

well it would not be fun any other way:)

swissgirl · Answer

hahahah true I just learn it and never have time to digest nething. I am always running behind. Wish there was more time on my hands

dumbcow · Answer

if you had to this by hand without graphing software...i would approximate using Newtons method for finding zeros
$$x_{n+1} =x_{n}-\frac{f(x_{n})}{f'(x_{n})} $$
Let f(x) = 3^x -x-4 , then f'(x) = 3^x ln(3) - 1