Exponent variables w/ out logs help

I have been looking hard online ect. for help regarding solving questions asking me find a variable which is an exponent without using logs. I have no idea how to manipulate a formula to solve these problems, and I would greatly respect any help. (Crying) example question: x^P/x^-2 = x^5/2 Find P

Re: Exponent variables w/ out logs help

Use the index law $\displaystyle \displaystyle \begin{align*} \frac{a^m}{a^n} = a^{m-n} \end{align*}$ to simplify the LHS, then you can set the exponents equal to each other and solve for P.

Re: Exponent variables w/ out logs help

Thank you, although I am still having a brain fart when it comes to the simplified form. I followed that law to get x^P+2 = x^5/2. I then subtracted 2 ( after making denominators the same) x^P+ 4/2 - 4/2 = x^ 5/2 - 4/2 I am left with x^P = x^1/2 Therefore p must equal 1/2 Am I correct?

Re: Exponent variables w/ out logs help

You REALLY need to work on setting out your algebra correctly. I can see that your thinking is correct, and you ended up with the right answer of P = 1/2, but it is set out so badly that it's almost unreadable... It should be

$\displaystyle \displaystyle \begin{align*} \frac{x^P}{x^{-2}} &= x^{\frac{5}{2}} \\ x^{P - (-2)} &= x^{\frac{5}{2}} \\ x^{P + 2} &= x^{\frac{5}{2}} \\ P + 2 &= \frac{5}{2} \\ P + \frac{4}{2} &= \frac{5}{2} \\ P &= \frac{1}{2} \end{align*}$