SOLUTION: How do you solve Log (3x) base 5 + log(x-3) base 5= log 30 base 5

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Question 1036380: How do you solve
Log (3x) base 5 + log(x-3) base 5= log 30 base 5
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28+5%2C+3x+%29+%2B+log%28+5%2C+x-3+%29+=+log%28+5%2C+30+%29+
Use the rule:
+log%28+a%2Ab+%29+=+log%28+a+%29+%2B+log%28+b+%29+
----------------
+log%28+5%2C+3x%2A%28x-3%29+%29+=+log%28+5%2C+30+%29+
+3x%2A%28+x-3+%29+=+30+
+3x%5E2+-+9x+=+30+
+x%5E2+-+3x+=+10+
complete the square
+x%5E2+-+3x+%2B+%28+3%2F2+%29%5E2+=+10+%2B+%28+3%2F2+%29%5E2+
+x%5E2+-+3x+%2B+9%2F4+=+10+%2B+9%2F4+
+%28+x+-+3%2F2+%29%5E2+=+49%2F4+
+%28+x+-+3%2F2+%29%5E2+=+%28+7%2F2+%29%5E2+
Take the square root of both sides
+x+-+3%2F2+=+7%2F2+
+x+=+10%2F2+
+x+=+5+
and, also:
+x+-+3%2F2+=+-7%2F2+
+x+=+-4%2F2+
+x+=+-2+
----------------------
check the answers:
+x+=+5+
+log%28+5%2C+3x+%29+%2B+log%28+5%2C+%28x-3%29+%29+=+log%28+5%2C+30+%29+
+log%28+5%2C+3%2A5+%29+%2B+log%28+5%2C+%285-3%29+%29+=+log%28+5%2C+30+%29+
+log%28+5%2C+15+%29+%2B+log%28+5%2C+2+%29+=+log%28+5%2C+30+%29+
+log%28+5%2C+15%2A2+%29+=+log%28+5%2C+30+%29+
+log%28+5%2C+30+%29+=+log%28+5%2C+30+%29+
OK
-------------
+x+=+-2+
+log%28+5%2C+3x+%29+%2B+log%28+5%2C+x-3+%29+=+log%28+5%2C+30+%29+
+log%28+5%2C+3%2A%28-2%29+%29+%2B+log%28+5%2C+%28-2-3%29+%29+=+log%28+5%2C+30+%29+
This answer doesn't work. You can't raise +5+ to
a real exponent and get a negative result