SOLUTION: What is x in log base 5 (x+1) + log base 5(x+21) =3

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Question 886057: What is x in log base 5 (x+1) + log base 5(x+21) =3
Found 2 solutions by lwsshak3, MathTherapy:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
What is x in log base 5 (x+1) + log base 5(x+21) =3
log%285%2C%28x%2B1%29%29%2Blog%285%2C%28x%2B21%29%29=3
log%285%2C%28%28x%2B1%29%28x%2B21%29%29%29=3
(x+1)(x+21)=5^3=125
x^2+22x+441=125
x^2+22x+316=0
solve for x by quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=1, b=22, c=316
no real solution:
b^2-4ac<0

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
What is x in log base 5 (x+1) + log base 5(x+21) =3


log+%285%2C+%28x+%2B+1%29%29+%2B+log+%285%2C+%28x+%2B+21%29%29+=+3

log+%285%2C+%28x+%2B+1%29%28x+%2B+21%29%29+=+3

log+%285%2C+%28x%5E2+%2B+22x+%2B+21%29%29+=+3

x%5E2+%2B+22x+%2B+21+=+5%5E3

x%5E2+%2B+22x+%2B+21+=+125+

x%5E2+%2B+22x+-+104+=+0

(x - 4)(x + 26) = 0

x – 4 = 0			OR			x + 26 = 0

highlight_green%28highlight_green%28x+=+4%29%29				OR			x = - 26 (ignore) 

You can do the check!! 



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