Question 220516: Can anyone help me?
Solve for x:
log(subscript 3) x^9 = -3
Answer by likaaka(51)   (Show Source):
You can put this solution on YOUR website! This is the basic logarithmic relationship y=b^x is equivalent to log(subscript b)(y)=x
So in your problem log(subscript 3) x^9 = -3 is equivalent to x^9=3^(-3)
To solve for x, first get rid of the negative exponent
x^9 = 1/(3^3), simplify
x^9 = 1/27, now take the 9th root of both sides
root9 of x^9 = root9 of (1/27), simplify **sorry couldn't figure out the html code
x = 1/(root 9 of 27), now since you shouldn't have radicals in the denominator you must rationalize the denominator
There are three 3s in 27 ie 3*3*3=27, so to rationalize the denominator, we need six more 3s to get rid of the radical. Multiply top and bottom by the 9th root of 3*3*3*3*3*3 or 3^6
1/(9th root of 3^3) * (9th root of 3^6)/(9th root of 3^6) =
(9th root of 3^6)/(9th root of 3^9), simplfy
(9th root of 3^6)/3
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