Question #55de4

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Question #55de4

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Answer 1 · 2016-11-14T10:29:18

Assuming you meant ${log}_{a} (\frac{a}{\sqrt{x}}) - {log}_{a} (\sqrt{a} x)$ $log_a(a/sqrtx)-log_a(sqrtax)$

$\frac{1}{2} - \frac{3}{2} {log}_{a} x$ $1/2-3/2log_ax$

Explanation:

${log}_{a} (\frac{a}{\sqrt{x}}) - {log}_{a} (\sqrt{a} x) = {log}_{a} ⎛ ⎝ \frac{\frac{a}{\sqrt{x}}}{\sqrt{a} x} ⎞ ⎠ = {log}_{a} (\frac{\sqrt{a}}{x \sqrt{x}}) = {log}_{a} \sqrt{a} - {log}_{a} x^{\frac{3}{2}} = \frac{1}{2} - \frac{3}{2} {log}_{a} x$ $log_a(a/sqrtx)-log_a(sqrtax)=log_a((a/sqrtx)/(sqrtax))=log_a(sqrta/(x sqrtx))=log_asqrta-log_ax^(3/2)=1/2-3/2log_ax$

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Question #55de4

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