SOLUTION: log 3=2 with log base x-1

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Question 446837: log 3=2 with log base x-1
Found 2 solutions by chriswen, mohammadrezai:
Answer by chriswen(106) About Me  (Show Source):
You can put this solution on YOUR website!
log 3=2 with log base x-1
%28x-1%29%5E2=3
x%5E2-2x%2B1=3
x%5E2-2x%2B1-3=0
x%5E2-2x-2=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-2+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-2=12.

Discriminant d=12 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+12+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+12+%29%29%2F2%5C1+=+2.73205080756888
x%5B2%5D+=+%28-%28-2%29-sqrt%28+12+%29%29%2F2%5C1+=+-0.732050807568877

Quadratic expression 1x%5E2%2B-2x%2B-2 can be factored:
1x%5E2%2B-2x%2B-2+=+1%28x-2.73205080756888%29%2A%28x--0.732050807568877%29
Again, the answer is: 2.73205080756888, -0.732050807568877. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-2+%29

Answer by mohammadrezai(14) About Me  (Show Source):
You can put this solution on YOUR website!
Log a on base b equal c means
b%5Ec=a there for
=%28x-1%29%5E2=3
x-1=+-√3
that x=1-sqrt%283%29 is not acceptable
=x=1%2Bsqrt%283%29is answer.