SOLUTION: Given x > 1, solve for x (log x^7)(log x) − log x^2 − 5 = 0

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Question 985278: Given x > 1, solve for x
(log x^7)(log x) − log x^2 − 5 = 0
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
log%28x%5E7%29%2Alog%28x%29+-+log%28x%5E2%29+-+5+=+0
7%2Alog%28x%29%2Alog%28x%29+-+2%2Alog%28x%29+-+5+=+0+
+7%2Alog%28x%29%5E2+-+2+log%28x%29+-+5+=+0
Let +y+=+log%28x%29+
+7y%5E2+-+2y+-+5+=+0
Use quadratic formula
y+=+%28-%28-2%29+%2B-+sqrt%28%28-2%29%5E2+-+4%2A7%2A%28-5%29%29%29%2F%282%2A7%29
y+=+%282+%2B-+sqrt%284%2B140%29%29%2F14
y+=+%282+%2B-+12%29+%2F+14
+y+=+-6%2F14+%2C+1+
First, deal with y+=+-6%2F14
y+=+-6%2F14
log%28x%29+=+-6%2F14
x+=+10%5E%28-6%2F14%29+=+.373
Now deal with y+=+1
y+=+1
log%28x%29+=+1
x+=+10%5E1+=+10
Since .373+%3C+1, then we only accept highlight%28x+=+10%29