SOLUTION: Solve the equation 1/(7^x)= 3*49^(5-x), giving your answer in the form a+ log(base 7)b where a,b are integers.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve the equation 1/(7^x)= 3*49^(5-x), giving your answer in the form a+ log(base 7)b where a,b are integers.      Log On


   

Question 1044778: Solve the equation 1/(7^x)= 3*49^(5-x), giving your answer in the form a+ log(base 7)b where a,b are integers.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
7%5E%28-x%29=3%2A%287%5E2%29%5E%285-x%29

7%5E%28-x%29=3%2A7%5E%2810-2x%29

log%28%287%5E%28-x%29%29%29=log%28%283%29%29%2B%2810-2x%29%2Alog%28%287%29%29

-x%2Alog%28%287%29%29=log%28%283%29%29%2B%2810-2x%29%2Alog%28%287%29%29

REMINDER: base is 7.

-x=log%28%283%29%29%2B10-2x

2x-x=log%28%283%29%29%2B10

highlight%28x=log%287%2C3%29%2B10%29

system%28a=10%2Cb=3%29