# Solving for a negative exponent

Is it possible to solve for a negative exponent? If so, can someone help me get the n on one side of the equation?

I'm not a math student and I have no math teacher connections so I thought I would turn here when I was unable to find the answer myself on Google.

The equation calculates monthly car payments ($$m$$) from interest rate ($$i$$), principal ($$p$$) and number of months ($$n$$). I figured out how to solve for $$p$$ if I have all the other values. I assume $$i$$ is impossible to solve for, but $$n$$ looked like it might be possible.

?I'm not really sure about the math terms either if someone wants to help and put the correct tags.

$$\frac{\frac{i}{12}\times p}{1-\left(1+\frac{i}{12}\right)^{-n}} = m$$

• If you know all the other values, you can find $n$, using logarithms – Henry May 3 '16 at 7:57
• Any idea what that equation might look like? – Tyler May 3 '16 at 8:02
• You could multiply both sides of the equation by the denominator in order to cancel it on the left side. Then, isolate the term with the $n$ on the right side, and take a logarithm of both sides. Then you can bring down the n and divide by the logarithm to completely isolate $n$ – Ovi May 3 '16 at 8:08

$a^{-b} = \frac{1}{a^b}$