SOLUTION: log(base4)(x-3)+log(base4)(x+9)=3

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Question 757101: log(base4)(x-3)+log(base4)(x+9)=3
Found 2 solutions by tommyt3rd, josmiceli:
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
please repost to state a complete question - what is to be done?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28+4%2C+x-3+%29+%2B+log%28+4%2C+x%2B9+%29+=+3+
Make the substitution:
+3+=+log%28+4%2C+64+%29+
+log%28+4%2C+x-3+%29+%2B+log%28+4%2C+x%2B9+%29+=+log%28+4%2C+64+%29+
+log%28+4%2C++%28+x-3+%29%2A%28+x%2B9+%29+%29+=+log%28+4%2C+64+%29+
+%28+x-3+%29%2A%28+x%2B9+%29+=+64+
+x%5E2+-+3x+%2B+9x+-+27+=+64+
+x%5E2+%2B+6x+-+91+=+0+
Use quadratic formula
+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+6+
+c+=+-91+
+x+=+%28-6+%2B-+sqrt%28+6%5E2+-+4%2A1%2A%28-91%29+%29%29+%2F+%282%2A1%29+
+x+=+%28-6+%2B-+sqrt%28+36+%2B+364+%29%29+%2F+2+
+x+=+%28-6+%2B-+sqrt%28+400+%29%29+%2F+2+
+x+=+%28+-6+%2B+20+%29+%2F+2+
+x+=+7+
and
+x+=+%28+-6+-+20+%29+%2F+2+
+x+=+-13+
This negative answer must be rejected because a
log to the base +4+ cannot give you a negative result
+x+=+7+ is the answer
check:
+log%28+4%2C+x-3+%29+%2B+log%28+4%2C+x%2B9+%29+=+3+
+log%28+4%2C+7-3+%29+%2B+log%28+4%2C+7%2B9+%29+=+3+
+log%28+4%2C+4+%29+%2B+log%28+4%2C+16+%29+=+3+
+1+%2B+2+=+3+
OK