SOLUTION: How do I solve this without a calculator? 1/27=3^2x

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Question 303926: How do I solve this without a calculator?
1/27=3^2x
Found 3 solutions by JBarnum, richwmiller, Alan3354:
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F27=3%5E2x
1%2F27=9x
%281%2F27%29%2827%2F1%29=9x%2827%2F1%29
1cross%28%281%2F27%29%2827%2F1%29%29=243x
1%2F243=x
3%5E2=3%2A3=9
9%2A27=9%2A20%2B9%2A7=180%2B63=243
multiplying by reciprical makes it easy without calculator.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
There are two things that you have to be able to see.
You have to know that 27 is a power of 3
27=3^3
you have to know that 1/27 is 1/3^3 and also 3^(-3)
1/27=3^(-3)
so we have 3^(-3)=3^2x
2x=-3
x=-1.5

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
It could be either of the 2 solutions.
Parentheses are free. Use some.