SOLUTION: Log base 3 (3x+18)=log base 3 (x squared+x)

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Question 729721: Log base 3 (3x+18)=log base 3 (x squared+x)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

if log%283%2C+%283x%2B18%29%29=log%283%2C+%28x%5E2%2Bx%29%29
than
3x%2B18=x%5E2%2Bx....solve for x
0=x%5E2-3x%2Bx-18
x%5E2-2x-18=0.....use quadratic formula

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+...note, a=1, b=-2, and c=-18

x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A%28-18%29+%29%29%2F%282%2A1%29+


x+=+%282+%2B-+sqrt%28+4%2B72+%29%29%2F2+

x+=+%282+%2B-+sqrt%28+76+%29%29%2F2+

x+=+%282+%2B-+sqrt%284%2A19+%29%29%2F2+

x+=+%282+%2B-+2sqrt%2819+%29%29%2F2+
x+=+%28cross%282%291+%2B-+cross%282%29sqrt%2819+%29%29%2Fcross%282%29+

x+=+%281+%2B-+sqrt%2819+%29%29+
x+=+%281+%2B-+4.35889894354%29+
solutions:
x+=+1+%2B+4.35889894354+
x+=5.35889894354+

x+=5.36+
or
x+=+1+-+4.35889894354
x+=+-3.35889894354
x+=+-3.36