SOLUTION: logx(9)=-1/3

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Question 62745: logx(9)=-1/3
Found 2 solutions by funmath, joyofmath:
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
logx(9)=-1/3
x^(-1/3)=9
(x^(-1/3))^-3=9^-3
x=1/9^3
highlight%28x=1%2F729%29
Check:
log(1/729)(9)=-1/3
log(9)/log(1/729)=-1/3
-1/3=-1/3 We're right!
Happy Calculating!!!

Answer by joyofmath(189) About Me  (Show Source):
You can put this solution on YOUR website!
logx(9)=-1/3
If logx(9)=-1/3 then x%5E%28-1%2F3%29=9.
Cube both sides. Then, %28x%5E%28-1%2F3%29%29%5E3=9%5E3.
Or, x%5E-1+=+9%5E3.
Now, raise both sides to the -1 power.
Then, %28x%5E-1%29%5E-1+=+%289%5E3%29%5E-1.
Or, x=9%5E-3 or x=1%2F9%5E3=1%2F279.
To verify the answer plug x=9%5E-3 into x%5E%28-1%2F3%29=9
and you get %289%5E-3%29%5E%28-1%2F3%29+=+9%5E%283%2A1%2F3%29+=+9%5E1+=+9.