If f(0) = 5 and f(6) = 23, using the form f(x) = $\displaystyle Pa^x$, find the value of P, and then find the value of a.

So far, I have:

$\displaystyle f(6) = Pa^6 = 23$

$\displaystyle P = 23/a^6$

Then I try to solve for a:

$\displaystyle f(0) = Pa^0 = 5$

Is this the right way to go about things? If I plug in my value for P I get:

$\displaystyle (23/a^6)*a^0 = 5$

$\displaystyle (23/a^6)*1 = 5$

$\displaystyle (23/a^6)*1 = 5$

$\displaystyle 23/5 = a^6$

Is this the right process? Now how do I solve for a?

$\displaystyle log 23/5 = 6 log a$ ??