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evaluate
[tex]f(x)=0.5 log_{8}(x) [/tex]
if x=12352

round 2 decimal points

please help ive done this twice and gotten 2 wrong answers

Respuesta :

faryna

[tex] = \frac{1}{2} log_{ {2}^{3} }(12352) [/tex]
[tex] = \frac{1}{2} \times \frac{1}{3} log_{2}(12352) [/tex]
[tex] = \frac{1}{6} log_{2}(12352) [/tex]
[tex] = 2.26541[/tex]
[tex]2.27[/tex]

[tex] \bf \textit{Logarithm Change of Base Rule}
\\\\
log_a b\implies \cfrac{log_c b}{log_c a}\\\\
-------------------------------\\\\
f(x)=0.5log_8(x)\implies \stackrel{x=12352}{f(12352)=0.5log_8(12352)}
\\\\\\
f(12352)=\stackrel{\textit{change of base rule}}{0.5\cdot \cfrac{log_{10}(12352)}{log_{10}(8)}}\implies f(12352)\approx 2.265409506211346737 [/tex]

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