SOLUTION: please solve for x log cube root of x= square root of log x

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Question 183941: please solve for x
log cube root of x= square root of log x

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
please solve for x
log cube root of x = square root of log x
:
You can write it using exponent for cube root
log%28x%5E%281%2F3%29%29+=+sqrt%28log%28x%29%29
log equiv of exponent
%281%2F3%29log%28x%29+=+sqrt%28log%28x%29%29
:
Let r = log(x) and rewrite the above equation using r
%281%2F3%29r+=+sqrt%28r%29
Multiply both sides by 3
r+=+3%2Asqrt%28r%29
square both sides
r^2 = 9r
divide both sides by r
r = 9
:
replacing r with log(x):
log(x) = 9
find the 10%5Ex of 9
x = 1,000,000,000
;
:
Check for equality on a calc:
enter: log(1000000000^(1/3)) = 3
and
enter: sqrt%28log%281000000000%29%29 = 3 also