SOLUTION: Can anyone help me? Solve for x: log(subscript 3) x^9 = -3

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
RELATED QUESTIONS
Can anyone help me solve {{{ log(x)12 = 3... (answered by addingup,MathTherapy)

solve for x. log(subscript 3)(x^2+5x)-log(subscript... (answered by edjones)

Can someone please help me? Solve for x in terms of k log{subscript 5}x +... (answered by stanbon)

can anyone help me solve the following log equation: Solve for x: 2^(x-1) =... (answered by jsmallt9)

please help me solve for x algebraically: log subscript 2 x + log subscript 2 (x+2)... (answered by nerdybill,lwsshak3)

need help solving log subscript 3(10x-1) - log subscript... (answered by Nate)

Hello, Could someone please help me simplify these logarithms/ 1.... (answered by stanbon)

Graph y=log(subscript 3)(x). PLEASE... (answered by vleith)

Hello all! Can someone please help me ASAP! Condense the following... log3 2x+3... (answered by stanbon)