SOLUTION: solve the simultaneous equation (A) Logx=y=1/2log(2x-1) all log is in base 3 (B) logx=y=log(2x-1),the first log is in base 3 while the second log is in base 9

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: solve the simultaneous equation (A) Logx=y=1/2log(2x-1) all log is in base 3 (B) logx=y=log(2x-1),the first log is in base 3 while the second log is in base 9      Log On


   

Question 1086577: solve the simultaneous equation
(A) Logx=y=1/2log(2x-1) all log is in base 3
(B) logx=y=log(2x-1),the first log is in base 3 while the second log is in base 9
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1.
log%283%2Cx%29=y=%281%2F2%29log%283%2C%282x-1%29%29+
log%283%2Cx%29=log%283%2C%282x-1%29%5E%281%2F2%29%29+
log%28x%29%2Flog%283%29=log%28%282x-1%29%5E%281%2F2%29%29%2Flog%283%29+
log%28x%29=log%28sqrt%282x-1%29%29+
x=sqrt%282x-1%29+
x%5E2=%28sqrt%282x-1%29%29%5E2+
x%5E2=2x-1+
x%5E2-2x%2B1=0+
%28x-1%29%5E2=0+
x-1=0+
x=1+

2.
log%283%2Cx%29=y=%281%2F2%29log%289%2C%282x-1%29%29+
log%283%2Cx%29=log%289%2C%282x-1%29%5E%281%2F2%29%29+
log%28x%29%2Flog%283%29=log%28%282x-1%29%5E%281%2F2%29%29%2Flog%289%29+
log%28x%29%2Flog%283%29=log%28sqrt%282x-1%29%29%2Flog%283%5E2%29+
log%28x%29%2Flog%283%29=log%28sqrt%282x-1%29%29%2F2log%283%29+
2log%28x%29%2F2log%283%29=log%28sqrt%282x-1%29%29%2F2log%283%29+
2log%28x%29=log%28sqrt%282x-1%29%29
log%28x%5E2%29=log%28sqrt%282x-1%29%29
x%5E2=sqrt%282x-1%29
x%5E4=2x-1
x%5E4-2x%2B1=0
%28x+-+1%29+%28x%5E3+%2B+x%5E2+%2B+x+-+1%29+=+0
solutions:
x=1


Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

solve the simultaneous equation
(A) Logx=y=1/2log(2x-1) all log is in base 3
(B) logx=y=log(2x-1),the first log is in base 3 while the second log is in base 9
AMBIGUOUS! 

If you need a correct answer (I would imagine you would), then fix and re-post!