How to solve the inequality $$x+3^x<4$$

This problem is found in Spivak's calculus, ch 1 - the highly praised work - which is supposed to be a gentle introduction for beginners in mathematics.

Please do not tell me that it cannot be solved algebraically and one needs to use Lambert's function. I have heard of Lambert's function and understand that it requires some advanced knowledge of differential equations. Neither me nor the average student of Spivak's calculus is that advanced to know that stuff.

Thanks in advance.

  • 2
    $\begingroup$ But if you don't want answer with the Lambert's W function why did you use that tag ? $\endgroup$ – Renato Faraone May 11 '15 at 19:49
  • $\begingroup$ sorry about that, did not want to cause any inconveniences $\endgroup$ – Eugene May 12 '15 at 11:55

$$x < 1$$ Because $x+3^x$ is increasing, and it equals 4 at x = 1. So for $x<1$ the inequality holds.


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