if-x-2-y-3-find-log-x-x-y-

Question Number 146459 by mathdanisur last updated on 13/Jul/21

i f x^{2} = y^{3} f i n d {l o g}_{x} x \sqrt{y} = ?

Answered by MJS_new last updated on 13/Jul/21

\log_{x} x \sqrt{y} = \frac{\ln x \sqrt{y}}{\ln x} = \frac{\ln x + \frac{1}{2} \ln y}{\ln x} = 1 + \frac{\ln y}{2 \ln x} =

[y = x^{2 / 3}]

= 1 + \frac{\ln x^{2 / 3}}{2 \ln x} = 1 + \frac{\frac{2}{3} \ln x}{2 \ln x} = 1 + \frac{1}{3} = \frac{4}{3}

Commented by mathdanisur last updated on 13/Jul/21

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