# Inequality with exponent variable

Is there any way to isolate $n$ algebraically in this inequality? I've managed to find it graphically, but I'm lost on how I would apply algebra to this question.

$$10000+800n>10000\times1.05^n$$

• Apply logarithms to both sides, then subtract getting one side with the logs being > 0 is one way to go about it. – OLE Nov 29 '16 at 5:25
• @ELO, this will not work, as you have a sum inside a log. There is no way to solve for $n$ analytically without heavy machinery like the Lambert function. The approximate positive solution is $18.8376245\ldots$. – vadim123 Nov 29 '16 at 5:33
• If you're interested in integer domain, then a cubic approximation to RHS will suffice, and is analytically solvable. It looks like when simple interest at 8% compares to compound interest at 5%, so perhaps all you need is integers. – Macavity Nov 29 '16 at 5:47