How do you simplify ${log}_{5} {\sqrt{2}}^{2}$ $log_ 5 sqrt2^2$ ?

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How do you simplify ${log}_{5} {\sqrt{2}}^{2}$ $log_ 5 sqrt2^2$ ?

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Answer 1 · 2016-03-22T18:30:50

${log}_{5} {\sqrt{2}}^{2} \approx 0.43$ $log_5 sqrt2^2~~0.43$

Explanation:

${log}_{5} {\sqrt{2}}^{2}$ $log_5 sqrt2^2$
$= {log}_{5} 2$ $=log_5 2$
$= \frac{log 2}{log 5}$ $=log2/log5$ -> use property ${log}_{b} x = \frac{log x}{log b}$ $log_bx=logx/logb$
$\approx 0.43$ $~~0.43$

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How do you simplify ${log}_{5} {\sqrt{2}}^{2}$ $log_ 5 sqrt2^2$ ?

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