Solving a specific equation in Mathematica & Finding the range of a value in an inequality

Question

Is there any way to solve (or even approximate the value of x) the following equation in Mathematica?

Solve[x - 11 - (1.0002)(0.0011/5.001)^(3x/(3x-5.0001)) == 0, x, Reals]

I have also another question which is in the following inequality how can I find the range of m that satisfies the inequality?

m - 2 - (0.02/5)^(m/(m-2)) > 0 && m > 0

Coolwater · Accepted Answer · 2019-07-27 18:47:44Z

0

The first one works the way you have written unless x has some definition that breaks it.
Try Remove[x] and then evaluate it again.

For the second one write:

Reduce[m - 2 - (2/100/5)^(m/(m - 2)) > 0 && m > 0, m, Reals]

m > 2

answered Jul 27, 2019 at 18:47

Coolwater

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$\begingroup$ Thanks for your quick reply. For the first equation whenever I try to solve it I faced the following message: "Solve::ratnz: Solve was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result. $\endgroup$
– Shirin elahi
Commented Jul 27, 2019 at 19:12
$\begingroup$ Try this Solve[Rationalize[ x - 11 - (1.0002) (0.0011/5.001)^(3 x/(3 x - 5.0001)) == 0], x, Reals] // N[#, 10] & $\endgroup$
– Rohit Namjoshi
Commented Jul 28, 2019 at 2:12
$\begingroup$ Thank you so much @RohitNamjoshi. It works perfectly. $\endgroup$
– Shirin elahi
Commented Jul 28, 2019 at 3:54

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