SOLUTION: how would i go about answering this question: solve for x using logarithms: 9^2x * 9 = (27^2x)/27

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Question 577682: how would i go about answering this question:
solve for x using logarithms:
9^2x * 9 = (27^2x)/27
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+9%5E%282x%29+%2A+9+=+%2827%5E%282x%29%29%2F27+
I would rewrite this as:
+9%5E%28+2x+%2B+1%29+=+27%5E%282x%29+%2A+27%5E%28-1%29+
+9%5E%28+2x+%2B+1+%29+=+27%5E%28+2x+-+1+%29+
Now I can say +27+=+9%5E%283%2F2%29+
This is true because +9%5E%281%2F2%29+=+3+ and
+3%5E3+=+27+
+9%5E%28+2x+%2B+1+%29+=+%28+9%5E%283%2F2%29%29%5E%28+2x+-+1+%29+
+9%5E%28+2x+%2B+1+%29+=+9%5E%28+3x+-+3%2F2+%29+
Take the log to base 9 of both sides
+2x+%2B+1+=+3x+-+3%2F2+
+x+=+2%2F2+%2B+3%2F2+
+x+=+5%2F2+
check answer:
+9%5E%282x%29+%2A+9+=+%2827%5E%282x%29%29%2F27+
+9%5E%282%2A5%2F2%29+%2A+9+=+%2827%5E%282%2A5%2F2%29%29%2F27+
+9%5E5+%2A+9+=+27%5E5+%2F+27+
+9%5E6+=+27%5E4+
+9%5E6+=+%283%5E3%29%5E4+
+%283%5E2%29%5E6+=+3%5E12+
+3%5E12+=+3%5E12+
OK