pre-calculus question
x + 3^x

Question

pre-calculus question
x + 3^x < 4
from the graph or by testing you can see that x<1
but is there any algebrical solution to this?i mean with logs for example

amistre64 · Answer

logs

anonymous · Answer

how?!

anonymous · Answer

there is no identity for log(x+3^x)

amistre64 · Answer

thats what im thinking, have to iron out the thought now :)

amistre64 · Answer

if we base each side
$$e^{x+3^x}=e^4$$
$$e^{x}e^{3^x}=e^4$$
hmmm

amistre64 · Answer

i got nothing at the moment.  maybe a ratio of derivative ... but ive never grasped that concept

anonymous · Answer

its from a book that the derivatives are after that chapter and should be easy..so i suppose its from the graph or by testing and the solutions manual says just x<1

amistre64 · Answer

setting up a linear approximation and taking the limit of it should get us there (just fancy trial and error really), but without a derivative to work with its just your usual trial and error

anonymous · Answer

yeah and the graphs even are at +3 chapters after that so i think its just trial and error...ty

amistre64 · Answer

youre welcome