SOLUTION: Please give formulas used and step explanations. Solve for X: Log(7x+1)=log(x-2)+1 Thank you very much.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please give formulas used and step explanations. Solve for X: Log(7x+1)=log(x-2)+1 Thank you very much.      Log On


   

Question 833593: Please give formulas used and step explanations.
Solve for X:
Log(7x+1)=log(x-2)+1
Thank you very much.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for X:
log%28%287x%2B1%29%29=log%28%28x-2%29%29%2B1
log%28%287x%2B1%29%29-log%28%28x-2%29%29=1
negative sign means division in logs
log%28%28%287x%2B1%29%2F%28x-2%29%29%29=1
convert to exponential form: base(10) raised to log of number(1)=number((7x+1)/(x-2))
10^1=(7x+1)/(x-2)
10(x-2)=7x+1
10x-20=7x+1
3x=21
x=7
check:
log(7x+1)=log(50)≈1.69897
log(x+2)+1=log(5)+1=1.69897
left side=right side