Question

how to solve
$log \sqrt{c \sqrt{ \sqrt{ \sqrt{c} } } }$

Answer 1

hope it helps...... :)

Answer 2

$log_{\sqrt{c}}{\sqrt{\sqrt{\sqrt{c}}}}$
we know,
$\sqrt{x} = x^{\frac{1}{2}}$
$so, \sqrt{c}=c^{\frac{1}{2}}$
$\sqrt{\sqrt{\sqrt{c}}}=c^{\frac{1}{2\times2\times2}} = {c}^{ \frac{1}{8} }$
now,
$log_{\sqrt{c}}{\sqrt{\sqrt{\sqrt{c}}}}$
$= log_c^{\frac{1}{2}}c^{\frac{1}{8}} = \frac{1}{4} log_{c}(c)$
$=\frac{1}{4}$