SOLUTION: log2(x-1)+log2(x+10=3

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Question 311578: log2(x-1)+log2(x+10=3
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
I'll assume you meant log base 2:
++++log%282%2Cx-1%29%2Blog%282%2Cx%2B10%29=3
++++log%282%2C%28x-1%29%28x%2B10%29%29=3
++++%28x-1%29%28x%2B10%29=+2%5E3
++++x%5E2%2B10x-x-10+=+8+
++++x%5E2%2B9x-10+=+8+
++++x%5E2%2B9x-18+=+0+
Solve by applying the quadratic formula. Doing so yields:
x = {1.685, -10.685}
The negative solution is an extraneous solution leaving:
x = 1.685
Details of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B9x%2B-18+=+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=%289%29%5E2-4%2A1%2A-18=153.

Discriminant d=153 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-9%2B-sqrt%28+153+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%289%29%2Bsqrt%28+153+%29%29%2F2%5C1+=+1.68465843842649
x%5B2%5D+=+%28-%289%29-sqrt%28+153+%29%29%2F2%5C1+=+-10.6846584384265

Quadratic expression 1x%5E2%2B9x%2B-18 can be factored:
1x%5E2%2B9x%2B-18+=+1%28x-1.68465843842649%29%2A%28x--10.6846584384265%29
Again, the answer is: 1.68465843842649, -10.6846584384265. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B9%2Ax%2B-18+%29