Question

log1/32 base ✓2
$log1by32 \: base \sqrt{2}$
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Answer 1

$\rm \LARGE\color{pink} {Good \: morning}$

${ \huge{ \star}} \: \: \: \: \underline{\bf \LARGE{To \: \: Find : }}$

$\dashrightarrow \sf log_{ \sqrt{2} }( \frac{1}{32} ) = {?}^{}$

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${ \huge{ \star}} \: \: \: \: \underline{\bf \LARGE{Solution : }}$

$\: \: \: \: \: \circ \: \: \: \: \: \sf log_{ \sqrt{2} }( \frac{1}{32} ) {}^{}$

$\sf \implies \: log_{ \sqrt {2}}( {2}) {}^{ - 5}$

$\sf \implies \: log_{ \sqrt {2} }( 2) {}^ { - \frac{10} {2}}$

$\implies \sf \: log_{ \sqrt{2} }( \sqrt{2} ) {}^{ - 10}$

$\implies \sf { - 10} \: log_{ \sqrt{2} }( \sqrt{2} )$

$\: \: \: \: \: \: \: \: \therefore \underline{ \boxed{ \sf{ \: - 10 \: }}}$

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${ \huge{ \star}} \: \: \: \: \underline{\bf \LARGE{Formula \: \: Required : }}$

$\dashrightarrow \sf \: log_{a}(a) = 1$

$\sf \dashrightarrow \: log_{a}(x) {}^{n} = n \: log_{a}(x)$

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HOPE THIS IS HELPFUL...

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