- #1
brh2113
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All information, including the problem, is attached. So far I think I've proven by induction that [tex]log (a^r)[/tex] = [tex]r log (a) [/tex] whenever [tex] r [/tex] is an integer, but I need to prove this for all rational numbers [tex] r = p/q [/tex].
We're working with the functional equation that has the property that [tex]f(xy) = f(x) + f(y)[/tex], and we're supposed to prove the equality using this. My initial thoughts were to write [tex]f(x*x^{p/q - 1})[/tex] = [tex]f(x) + f(x^{p/q - 1})[/tex], but it didn't get me anywhere. Any thoughts or suggestions?
We're working with the functional equation that has the property that [tex]f(xy) = f(x) + f(y)[/tex], and we're supposed to prove the equality using this. My initial thoughts were to write [tex]f(x*x^{p/q - 1})[/tex] = [tex]f(x) + f(x^{p/q - 1})[/tex], but it didn't get me anywhere. Any thoughts or suggestions?