SOLUTION: log(x)- log(x-1)=1/2 The teacher says to solve for t in this one too but I see no t :(

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: log(x)- log(x-1)=1/2 The teacher says to solve for t in this one too but I see no t :(      Log On


   

Question 659947: log(x)- log(x-1)=1/2
The teacher says to solve for t in this one too but I see no t :(
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
log(x)- log(x-1)=1/2
The teacher says to solve for t in this one too but I see no t
**
teacher probably meant solve for x
log(x)- log(x-1)=1/2
place under single log
log[x/(x-1)]=1/2
convert to exponential form
10^(1/2)=x/(x+1)
square both sides
10=x^2/(x+1)^2
10(x+1)^2=x^2
10(x^2+2x+1)=x^2
10x^2+20x+10-x^2=0
9x^2+20x+10=0
solve for x using following quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=9, b=20, c=10
ans:
x=-0.613 or -2.721
reject, no solution:
x>0