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I am having trouble getting Mathematica to solve really simple inequalities.

I started with

Solve[{y^x >= 2*y - 1}, x]

but Mathematica can't solve it. So I tried

Solve[{y^x >= 2*y - 1, x > 10, y > 10}, x, Reals] 

with still no luck. I tried Reduce, but that didn't work either.

An obvious solution is $x \geq \frac{\ln(2y-1)}{\ln(y)}$. How can I persuade Mathematica to give me that?

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up vote 5 down vote accepted

You need to provide additional assumptions like in :

Reduce[{y^x >= 2*y - 1, y > 0, x > 0}, x, Reals]
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Oh.. Reduce[{y^x >= 2*y - 1, y > 10, x > 10}, x, Reals] doesn't work but that does. – Lembik Mar 17 '13 at 11:43

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