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