SOLUTION: sir i have a problem on solving this equation. i am trying to solve x and to simplify it. question: logx 8=-3? i convert it to exponential form x^-3=8 this are the formulas I'v

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: sir i have a problem on solving this equation. i am trying to solve x and to simplify it. question: logx 8=-3? i convert it to exponential form x^-3=8 this are the formulas I'v      Log On


   



Question 158892: sir i have a problem on solving this equation.
i am trying to solve x and to simplify it.
question: logx 8=-3?
i convert it to exponential form x^-3=8
this are the formulas I've tried to solve it but I'm not sure if it is correct.
a). (x^-3)^3=(8)^3
x=8^3
x=512:answer
b). i change the negative exponent to positive and transpose it to 8
x=8^3
x=512:answer
c). i get the reciprocal of the exponent and change it to 1/3
it became x^1/3=8
then i do: (cube root of x)^3 = (8)^3
i cancel out cube root of x and it became
x=8^3
x=512:answer
please help me to figure out the answer of this problem because I'm about to go crazy.
for my last question..
is this formula i have given is correct??
i mean is there any possible way to solve it??,,
thank you sir in advance..

Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
am trying to solve x and to simplify it.
question: logx 8=-3?8
i convert it to exponential form x^-3=8
Raise both sides to the -1/3 power:
(x^-3)^(-1/3) = 8^(-1/3)
x = (1/8)^(1/3)
x = 1/2
---------------------
Cheers,
Stan H.

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
there is an error in a) __ (x^-3)^3=x^-9 __ the exponents multiply

try (x^-3)^(-1/3)=8^(-1/3) __ x=8^(-1/3) __ x=1/2