SOLUTION: Show that if a and c are positive numbers with a not equal to c, {{{ a^x=c^q }}} , and {{{ c^y=a^z }}} , then xy=qz

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Show that if a and c are positive numbers with a not equal to c, {{{ a^x=c^q }}} , and {{{ c^y=a^z }}} , then xy=qz      Log On


   

Question 761218: Show that if a and c are positive numbers with a not equal to c, +a%5Ex=c%5Eq+ , and +c%5Ey=a%5Ez+ , then xy=qz
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
+a%5Ex=c%5Eq+ --> +%28a%5Ex%29%5Ey=%28c%5Eq%29%5Ey+ --> +a%5E%28xy%29=c%5E%28qy%29+
+c%5Ey=a%5Ez+ --> +%28c%5Ey%29%5Eq=%28a%5Ez%29%5Eq+ --> +c%5E%28yq%29=a%5E%28zq%29+ --> +c%5E%28qy%29=a%5E%28qz%29+
system%28a%5E%28xy%29=c%5E%28qy%29%2Cc%5E%28qy%29=a%5E%28qz%29%29 --> a%5E%28xy%29=a%5E%28qz%29 --> xy=qz