y-2-1-log-x-8-then-x-

Question Number 20245 by virus last updated on 24/Aug/17

y = 2^{\frac{1}{{l o g}_{x} 8}}

t h e n x = ?

Answered by Tinkutara last updated on 24/Aug/17

y = 2^{\log_{8} x} = 2^{\frac{1}{3} \log_{2} x}

y^{3} = 2^{\log_{2} x} = x

\Rightarrow x = y^{3}

Answered by Rauny last updated on 27/Jan/19

\frac{1}{(\frac{l n 8}{l n x})} = {l o g}_{2} y

\frac{l n x}{l n 8} = \frac{l n y}{l n 2}

l n x = \frac{l n 8}{l n 2} \cdot l n y = {l o g}_{2} 8 \cdot l n y

= 3 l n y

x = e^{3 l n y}

= y^{3}

∴ x = y^{3}

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