Solve inequality after specific variable

Question

I would appreciate if someone could help me solving the following inequality:

$$ \frac{p^s}{s+1} \ge d$$

We would like to solve the equation for $s$ and can assume that $p,s$ and $d$ are all positive and $p$ and $d$ can be seen as fix numbers.

Thank you!

Minor pedantry: this is not an equation, since you are not setting things equal to each other. This is an inequality. — Xander Henderson, Sep 18 '17 at 13:36
This is not an equation it is an inequality and it is not possible to solve in an algebraic way, but only with numerical/graphical methods. To to this we need actual values for the parameters $p,;d$ — Raffaele, Sep 18 '17 at 13:37

score 1 · Accepted Answer · answered Sep 18 '17 at 13:53

1

To make an example I set $\dfrac{2^s}{s+1}\ge 3$

Then I plotted the function $f(s)=\dfrac{2^s}{s+1}-3$ and found with numerical methods the intersections $s_1\approx -0.81;\;s_2\approx 3.87$

So I can say that the inequality is verified when $f(s)\ge 0$ that is $-1<s\le s_1\lor s\ge s_2$

Hope this is useful

answered Sep 18 '17 at 13:53

Raffaele

Thank you for your nice answer! I hoped for an algebraic method, but it seem not to be possible! – N. Younger Sep 18 '17 at 14:36

1 Answers1