SOLUTION: Solve for x: log (5x+ 6) = log (x-3) Please show me how you did it too. Thank you

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve for x: log (5x+ 6) = log (x-3) Please show me how you did it too. Thank you      Log On


   

Question 1130363: Solve for x:
log (5x+ 6) = log (x-3)
Please show me how you did it too. Thank you
Found 4 solutions by josgarithmetic, MathLover1, MathTherapy, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You would expect that log%28%28P%29%29=log%28%28V%29%29 should mean that P=V.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

log+%285x%2B+6%29+=+log+%28x-3%29-> if log and base same, we have
5x%2B+6+=+x-3
5x-x+=+-6-3
4x+=+-9
x+=+-9%2F4

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

Solve for x:
log (5x+ 6) = log (x-3)
Please show me how you did it too. Thank you
Correct answer: highlight_green%28matrix%281%2C2%2C+NO%2C+SOLUTION%29%29

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Both tutor @mathlover1 and tutor @josgarithmetic pointed out that if log(A) = log(B), then it should be true that A=B. They both overlooked that fact that A must be equal to B IF A SOLUTION EXISTS.

Tutor @maththerapy is right; there is no solution. That is because when you set A=B in this equation, you get x = -9/4. Then the equation says

log(-21/4) = log(-21/4)

But logs of negative numbers do not exist.

So, as tutor @maththerapy says: NO SOLUTION