SOLUTION: Solve for x if log base x 1/6=-1/2

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Question 1132594: Solve for x if log base x 1/6=-1/2
Found 3 solutions by ankor@dixie-net.com, MathLover1, rothauserc:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x if log base x 1/6=-1/2
log%28x%2C%281%2F6%29%29+=+-1%2F2
the exponent equiv of logs
x%5E%28-1%2F2%29+=+1%2F6
get rid of neg on exponent with the reciprocal
%281%2Fx%29%5E%281%2F2%29+=+1%2F6
square both sides
1%2Fx = 1%2F36
therefore
x = 36

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

log+%28x%2C+%281%2F6%29%29=-1%2F2+-> change to base 10

log+%28+%281%2F6%29%29%2Flog+%28%28x%29%29=-1%2F2+

log+%28+%281%2F6%29%29=-%281%2F2%29log+%28%28x%29%29+

log+%28+%281%2F6%29%29=log+%28%28x%5E%28-1%2F2%29%29%29+

log+%28%28+1%2F6%29%29=log+%28%281%2Fx%5E%281%2F2%29%29%29+

log+%28+%281%2F6%29%29=log+%28%281%2Fsqrt%28x%29%29%29+-> if log same, than

+1%2F6=1%2Fsqrt%28x%29+

+1%2Asqrt%28x%29=1%2A6+

+sqrt%28x%29=6+

+%28sqrt%28x%29%29%5E2=6%5E2+

+x=36+



Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
Use definition of logarithm
:
y = log base b (x), then x = b^y
:
-1/2 = log base x (1/6)
:
1/6 = x^(-1/2)
:
1/6 = 1/x^(1/2)
:
cross multiply the two fractions
:
x^(1/2) = 6
:
square both sides of =
:
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x = 36
:
check answer
:
log base base 36 (1/6) = -1/2
:
-1/2 = -1/2
:
answer checks
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