If X>1 then X^sqrt(X)/3=X^m. then find the value of m.

Answer Posted / 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)

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