SOLUTION: Express irrational solutions in exact form as a decimal rounded to three decimal places log2(3x+2)-log4x=3 (((log base 2 of (3x+2) - log base 4 of x =3)))

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Express irrational solutions in exact form as a decimal rounded to three decimal places log2(3x+2)-log4x=3 (((log base 2 of (3x+2) - log base 4 of x =3)))      Log On


   

Question 601556: Express irrational solutions in exact form as a decimal rounded to three decimal places

log2(3x+2)-log4x=3 (((log base 2 of (3x+2) - log base 4 of x =3)))
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
log2(3x+2)-log4x=3
convert to log base 2
log2(3x+2)-log2(x)/log2(4)=3
log2(4)=2
log2(3x+2)-log2(x)/2=3
LCD=2
2log2(3x+2)-log2(x)=6
place under single log
log2[(3x+2)^2/x)]=6
convert to exponential form
2^6=(3x+2)^2/x
64=(9x^2+12x+4)/x
64x=9x^2+12x+4
9x^2-52x+4=0
solve by quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=9, b=-52, c=4
x=.078
or
x=5.700