SOLUTION: (56*2^5x)/3^2x = (7*4^x*3^x)/27^x the answer must end up as for example: 7^x= 7^2x+3 they must have same base. then solve for x

Algebra ->  Exponents -> SOLUTION: (56*2^5x)/3^2x = (7*4^x*3^x)/27^x the answer must end up as for example: 7^x= 7^2x+3 they must have same base. then solve for x       Log On


   

Question 1079925: (56*2^5x)/3^2x = (7*4^x*3^x)/27^x
the answer must end up as for example: 7^x= 7^2x+3
they must have same base.
then solve for x
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

%2856%2A2%5E%285x%29%29%2F3%5E%282x+%29=+%287%2A4%5Ex%2A3%5Ex%29%2F%2827%5Ex+%29

%2856%2A2%5E%285x%29%29%2827%5Ex+%29=+7%2A12%5Ex%2A3%5E%282x+%29

%287%2A2%5E3%2A2%5E%285x%29%29%2827%5Ex+%29=+7%2A12%5Ex%2A3%5E%282x+%29

7+%2A2%5E%285x+%2B+3%29+27%5Ex=7%2A+108%5Ex................cancel 7, and since 108=4%2A27 we have

2%5E%285x+%2B+3%29%2A+27%5Ex=4%5Ex%2A27%5Ex+.............cancel 27%5Ex

2%5E%285x+%2B+3%29+=4%5Ex

2%5E%285x+%2B+3%29+=%282%5E2%29%5Ex

2%5E%285x+%2B+3%29+=2%5E%282x%29........if base same, we have

5x+%2B+3+=2x.............solve for x

5x-2x=-3

3x=-3

x=-1