How do you evaluate ${log}_{8} 4$ $log_8 4$ ?

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How do you evaluate ${log}_{8} 4$ $log_8 4$ ?

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Answer 1 · 2015-05-10T03:32:30

Consider that:
${log}_{a} (b) = x \to a^{x} = b$ $log_a(b)=x ->a^x=b$
in your case:
${log}_{8} (4) = x$ $log_8(4)=x$
So:
$8^{x} = 4$ $8^x=4$ that can be written as:
${(2^{3})}^{x} = 2^{2}$ $(2^3)^x=2^2$
$2^{3 x} = 2^{2}$ $2^(3x)=2^2$
so that:
$3 x = 2$ $3x=2$
and $x = \frac{2}{3}$ $x=2/3$

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How do you evaluate ${log}_{8} 4$ $log_8 4$ ?

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