Question

$log_{x}( \sqrt{x}$
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Answer 1

Answer:

$\log _x\left(\sqrt{x}\right)=\dfrac{1}{2}\quad \left(\mathrm{Decimal:\quad }\:0.5\right)$

Step-by-step explanation:

$\log _x\left(\sqrt{x}\right)$

$\gray{\mathrm{Rewrite\:as}}$

$=\log _x\left(x^{\dfrac{1}{2}}\right)$

$\gray{\mathrm{Apply\:log\:rule\:}\log _a\left(x^b\right)=b\cdot \log _a\left(x\right),\:\quad \mathrm{\:assuming\:}x\:\ge \:0}$

$=\dfrac{1}{2}\log _x\left(x\right)$

$\gray{\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1}$

$=\dfrac{1}{2}$

Answer 2

Answer:

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