How do you evaluate ${log}_{2} 8$ $log_2 8$ ?

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How do you evaluate ${log}_{2} 8$ $log_2 8$ ?

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Answer 1 · 2018-08-10T21:35:14

$3$ $3$

Explanation:

$using the law of logarithms$ $"using the "color(blue)"law of logarithms"$

$∙ x {log}_{b} x = n \Leftrightarrow x = b^{n}$ $•color(white)(x)log_b x=nhArrx=b^n$

$let {log}_{2} 8 = n \Leftrightarrow 8 = 2^{n} \Rightarrow n = 3$ $"let "log_2 8=nhArr8=2^nrArrn=3$

$\Rightarrow {log}_{2} 8 = 3$ $rArrlog_2 8=3$

Answer 2 · 2018-08-11T02:32:11

Using logarithm properties we have

${log}_{2} 8 = {log}_{2} 2^{3} = 3 \cdot {log}_{2} 2 = 3$ $log_2 8=log_2 2^3=3*log_2 2=3$

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