SOLUTION: Given that 3logx = y and log4x = y + 4, where x and y are real numbers, find the values of x and y. NOTE: The log is in base 2.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Given that 3logx = y and log4x = y + 4, where x and y are real numbers, find the values of x and y. NOTE: The log is in base 2.      Log On


   

Question 1134064: Given that 3logx = y and log4x = y + 4, where x and y are real numbers, find the values of x and y.
NOTE: The log is in base 2.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Given that 3log%282%2C%28x%29%29 = y and log%282%2C%284x%29%29 = y + 4, where x and y are real numbers, find the values of x and y.
:
rewrite
log%282%2C%28x%5E3%29%29+=+y
and
log%282%2C%284x%29%29+-4+=+y
y=y therefore
log%282%2C%284x%29%29+-+4 = log%282%2C%28x%5E3%29%29
rewrite to
log%282%2C%284x%29%29+-+log%282%2C%28x%5E3%29%29+=+4
which is
log%282%2C%28%284x%29%2Fx%5E3%29%29+=+4+
cancel x
log%282%2C%284%2Fx%5E2%29%29+=+4+
the exponent equiv
2%5E4+=+4%2Fx%5E2 = 16+=+4%2Fx%5E2
16x%5E2+=+4 = x%5E2+=+4%2F16 = x%5E2+=+1%2F4 = x+=+sqrt%281%2F4%29
x=1%2F2
:
find y
y+=+log%282%2C%28%281%2F2%29%5E3%29%29 = y+=+log%282%2C%28%281%2F8%29%29%29
exponent equiv
2%5Ey+=+1%2F8
y+=+-3
:
:
Check solutions in original 2nd equation: log%282%2C%284x%29%29+=+y+%2B+4,
log%282%2C%284%281%2F2%29%29%29+=+-3+%2B+4,
log%282%2C%282%29%29+=+1,