Question

Evaluate

Answer 1

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

Answer 2

$= \frac{1}{2} log_{ {2}^{3} }(12352)$
$= \frac{1}{2} \times \frac{1}{3} log_{2}(12352)$
$= \frac{1}{6} log_{2}(12352)$
$= 2.26541$
$2.27$