SOLUTION: need help on log equation: {{{(1/2)^(2x-1)=(1/4)^(3x+2)}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: need help on log equation: {{{(1/2)^(2x-1)=(1/4)^(3x+2)}}}      Log On


   

Question 630598: need help on log equation:
%281%2F2%29%5E%282x-1%29=%281%2F4%29%5E%283x%2B2%29
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F2%29%5E%282x-1%29=%281%2F4%29%5E%283x%2B2%29

Write %281%2F4%29 as %281%2F2%29%5E2

%281%2F2%29%5E%282x-1%29=%28%281%2F2%29%5E2%29%5E%283x%2B2%29

Remove outer parentheses on right by multiplying exponents:

%281%2F2%29%5E%282x-1%29=%281%2F2%29%5E%286x%2B4%29

Since the base 1%2F2 is the same on both sides and since 1%2F2 is
positive and not equal to 1, we may equate exponents:

2x-1 = 6x+4
 -4x = 5
   x = -5%2F4

No need for logs on this problems.  Logs could be used,
but they are unnecessary.

Edwin