SOLUTION: please help. Solve the following mathematically a. 3=4ln(x-2)= 11 b. log(13x-1)- log(x+2) + 1 c. solve the quadratic equation; 3x^2 - 4x-2=0 d. solve by factoring 2x^2+x-6=0

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: please help. Solve the following mathematically a. 3=4ln(x-2)= 11 b. log(13x-1)- log(x+2) + 1 c. solve the quadratic equation; 3x^2 - 4x-2=0 d. solve by factoring 2x^2+x-6=0      Log On


   

Question 455548: please help.
Solve the following mathematically
a. 3=4ln(x-2)= 11
b. log(13x-1)- log(x+2) + 1
c. solve the quadratic equation;
3x^2 - 4x-2=0
d. solve by factoring 2x^2+x-6=0
Thanks
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following mathematically
a. 3=4ln(x-2)= 11
Too many equal signs
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b. log(13x-1)- log(x+2) + 1
No equal sign, not an equation
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c. solve the quadratic equation;
3x^2 - 4x-2=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-4x%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=%28-4%29%5E2-4%2A3%2A-2=40.

Discriminant d=40 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+40+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+40+%29%29%2F2%5C3+=+1.72075922005613
x%5B2%5D+=+%28-%28-4%29-sqrt%28+40+%29%29%2F2%5C3+=+-0.387425886722793

Quadratic expression 3x%5E2%2B-4x%2B-2 can be factored:
3x%5E2%2B-4x%2B-2+=+%28x-1.72075922005613%29%2A%28x--0.387425886722793%29
Again, the answer is: 1.72075922005613, -0.387425886722793. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-4%2Ax%2B-2+%29

x+=+%282+-+sqrt%2810%29%29%2F3
x+=+%282+%2B+sqrt%2810%29%29%2F3
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d. solve by factoring 2x^2 + x - 6 = 0
(2x - 3)*(x + 2) = 0
x = -2, 3/2