SOLUTION: Dear Tutor Could you please help me with this investigation question from an old Maths Textbook? Please solve this inequation: {{{ 3^x > x^3 }}} The book only gives the

Algebra ->  Algebra  -> Exponents -> SOLUTION: Dear Tutor Could you please help me with this investigation question from an old Maths Textbook? Please solve this inequation: {{{ 3^x > x^3 }}} The book only gives the      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 134588: Dear Tutor
Could you please help me with this investigation question from an old Maths Textbook?
Please solve this inequation:
+3%5Ex+%3E+x%5E3+

The book only gives the answer: +x%21=3+. I tried to use "log" or "cube roots" to find out x but it seemed neither of them helped. Therefore, could you please show me how do you get +x%21=3+? Thank you in advance. :-)
Answer by stanbon(48535) About Me  (Show Source):
You can put this solution on YOUR website!
3^x > x^3
---------------
Graph the left side and the right side separately on the same set of axes:
graph%28400%2C300%2C-10%2C10%2C-10%2C15%2C3%5Ex%2Cx%5E3%29
----------
Observe where 3^x is above x^3:
Ans: x< 2.4780527...
-------------------------
I graphed them on a TI calculator so I could better analyze the problem.
-------------------------------
Cheers,
Stan H.