Answer / vidivelli

IF X>1

STEP:1
X^M=X^SQRT(X)/3 WE CAN WRITE IN OTHER WAY AS
M=SQRT(X)/3
SO SUBSTITUTE NUMBER 9,81 WHICH IS DIVISIBLE BY 3 AND
GREATER THAN 1
THEN
SUBSITTUTE X=81

M=SQRT(81)/3=9/3
M=3
SO X>1 SO X=81 M=3.

Answer / rafe saxon

1) Assuming that the current proposition uses implied
binding using the "mathematical/coding order of precedence"
for the operators, re-write explicitly (using parentheses):

(X^sqrt(X))/3 = X^m

2) Using "laws of logarithms":

log (a/b) = log(a) - log(b) -- quotient
log (a^b) = b*log(a) -- exponent

3) Hence:

m*log(X) = sqrt(X)*log(X) - log(3)

4) Finally, yields:

m = sqrt(X) - log(3)/log(X)

Answer / zak whaley

A quick and dirty direct proof can be used.

x^sqrt(x)/3 = x^m immediately yields that m = sqrt(x)/3.

Think of it simpler:
x^y = x^z you should easily see that y = z.

The "if x > 1" takes care of complex numbers as sqrt(x)
where x < 0 is complex.

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