SOLUTION: Log base 2 (8x) - log base 2 (x squared minus 1) = log base 2 3

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Question 703564: Log base 2 (8x) - log base 2 (x squared minus 1) = log base 2 3
Found 2 solutions by nerdybill, josmiceli:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Log base 2 (8x) - log base 2 (x squared minus 1) = log base 2 3
log%282%2C8x%29+-+log%282%2Cx%5E2-1%29+=+log%282%2C3%29
log%282%2C8x%2F%28x%5E2-1%29%29+=+log%282%2C3%29
8x%2F%28x%5E2-1%29+=+3
8x+=+3%28x%5E2-1%29
8x+=+3x%5E2-3%29
0+=+3x%5E2-8x-3
0+=+%283x%2B1%29%28x-3%29
x = {-1/3, 3}
we can throw out the negative solution (extraneous) leaving:
x = 3

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28+2%2C8x+%29+-+log%28+2%2C+%28x%5E2+-+1%29+%29+=+log%28+2%2C3+%29+
+log%28+2%2C+%288x%29+%2F+%28+x%5E2+-+1+%29+%29+=+log%28+2%2C3+%29+
+8x+%2F+%28+x%5E2+-+1+%29+=+3+
+3%2A%28+x%5E2+-+1+%29+=+8x+
+3x%5E2+-+3+-+8x+=+0+
+3x%5E2+-+8x+-+3+=+0+
Use the quadratic formula
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+3+
+b+=+-8+
+c+=+-3+
+x+=+%28+-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2+-+4%2A3%2A%28-3%29+%29%29+%2F+%282%2A3%29+
+x+=+%28+8+%2B-+sqrt%28+64+%2B+36+%29%29+%2F+6+
+x+=+%28+8+%2B-+sqrt%28+100+%29%29+%2F+6+
+x+=+%28+8+%2B+10+%29+%2F+6+
+x+=+18%2F6+
+x+=+3+
and
+x+=+%28+8+-+10+%29+%2F+6+
+x+=+-2%2F6+
+x+=+-1%2F3+
This negative result can't be used because of
+log%28+2%2C8x+%29+, which gives me
+log%282%2C+-8%2F3+%29+
The log to a positive base cannot give a negative result
The +x+=+3+ result is OK