SOLUTION: Solve log 4+ 2log x= 6

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Question 867028: Solve log 4+ 2log x= 6
Found 2 solutions by josmiceli, jim_thompson5910:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The key to solving this is to
recognize that +6+=+log%28%28+1000000+%29%29+
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+log%284%29+%2B+2%2Alog%28x%29+=+log%28%28+1000000+%29%29+
+2%2Alog%28x%29+=+log%28%28+1000000+%29%29+-+log%284%29+
+log%28%28x%5E2%29%29+=+log%28%28+10%5E6%2F4+%29%29+
+x%5E2+=+10%5E6%2F4+
+x+=+10%5E3%2F2+
+x+=+500+
( note that +-500+ does not work because
+2%2Alog%28%28+-500+%29%29+ makes no sense )
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You can check the answer with a calculator:
+log%284%29+%2B+2%2Alog%28x%29+=+6+
+.60206+%2B+2%2Alog%28x%29+=+6+
+2%2Alog%28x%29+=+6+-+.60206+
+2%2Alog%28x%29+=+5.39794+
+log%28x%29+=+2.69897+
+x+=+10%5E2.69897+
+x+=+499.999995+
close enough


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%284%29%29%2B2%2Alog%28%28x%29%29=6


log%28%284%29%29%2Blog%28%28x%5E2%29%29=6


log%28%284%2Ax%5E2%29%29=6


log%2810%2C%284%2Ax%5E2%29%29=6


4%2Ax%5E2=10%5E6


4%2Ax%5E2=1000000


x%5E2=250000


x=sqrt%28250000%29 Note: x%3E0 based on the domain of the log function


x=500