SOLUTION: Solve the equation and express the solution in exact form... log9(x-4)+log9(x-4)=1 This is what I have done... 9=(x-4)(x-4) 9=(x^2-4x-4x+16) -9 -9 0=(x^2-8x

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the equation and express the solution in exact form... log9(x-4)+log9(x-4)=1 This is what I have done... 9=(x-4)(x-4) 9=(x^2-4x-4x+16) -9 -9 0=(x^2-8x      Log On


   

Question 691267: Solve the equation and express the solution in exact form...
log9(x-4)+log9(x-4)=1


This is what I have done...
9=(x-4)(x-4)
9=(x^2-4x-4x+16)
-9 -9
0=(x^2-8x+7)
(x-7)(x-1)
x=7, x=1
not sure what Iam doing wrong.... Thanks!
Answer by MathTherapy(10858) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the equation and express the solution in exact form...
log9(x-4)+log9(x-4)=1

This is what I have done...
9=(x-4)(x-4)
9=(x^2-4x-4x+16)
-9 -9
0=(x^2-8x+7)
(x-7)(x-1)
x=7, x=1

not sure what Iam doing wrong.... Thanks!

log+%289%2C+%28x+-+4%29%29+%2B+log+%289%2C+%28x+-+4%29%29+=+1+

log+%289%2C+%28%28x+-+4%29%28x+-+4%29%29%29+=+1

%28x+-+4%29%28x+-+4%29+=+9%5E1

x%5E2+-+8x+%2B+16+=+9

x%5E2+-+8x+%2B+16+%96+9+=+0

x%5E2+-+8x+%2B+7+=+9

(x - 1)(x - 7) = 0

x = 1 (ignore as this value will result in a NEGATIVE log value)

highlight_green%28x+=+7+%29

Your answers are CORRECT. However, you need to do the check, which as you'll see will eliminate x+=+1 as a solution, thus leaving the only solution as x+=+7 (see above).

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