SOLUTION: solve (1/25)^-x=125^x-3. first i did 25^x=125^x-3. then 5^2x=5^3x-3. then 2X=3x-3 and x=3. but the answers supposed to be 9. please help, i have a test tomorow! thanks

Algebra ->  Exponents -> SOLUTION: solve (1/25)^-x=125^x-3. first i did 25^x=125^x-3. then 5^2x=5^3x-3. then 2X=3x-3 and x=3. but the answers supposed to be 9. please help, i have a test tomorow! thanks      Log On


   

Question 25353: solve (1/25)^-x=125^x-3. first i did 25^x=125^x-3. then 5^2x=5^3x-3. then 2X=3x-3 and x=3. but the answers supposed to be 9. please help, i have a test tomorow!
thanks
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F25%29%5E%28-x%29=125%5E%28x-3%29
%2825%29%5Ex+=+125%5E%28x-3%29

Now 25 is 5%5E2 and 125 is 5%5E3, so we have
%285%5E2%29%5Ex+=+%285%5E3%29%5E%28x-3%29
5%5E%282x%29+=+5%5E%283%28x-3%29%29

so we have 5 to a power on both sides and it is an equation, so the powers must be the same number, so 2x = 3(x-3)

Hence 2x = 3x-9
--> x = 9

jon