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

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


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

• 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. – Shirin elahi Jul 27 '19 at 19:12
• Try this Solve[Rationalize[ x - 11 - (1.0002) (0.0011/5.001)^(3 x/(3 x - 5.0001)) == 0], x, Reals] // N[#, 10] & – Rohit Namjoshi Jul 28 '19 at 2:12
• Thank you so much @RohitNamjoshi. It works perfectly. – Shirin elahi Jul 28 '19 at 3:54