Question

log2 log25 ^5
options are:
a.0 b.1 c.-1 d.1/2

Answer 1

log b (a) = {log c (a)} / { log c (b)}

using this relation ...

log2{log25(5)} = log2{log5(5) / log5(25)}

= log2{ 1 / 2}

= log2{2^(-1)}

= - log2{2}

= -1


so, option (c) -1 .. is the answer...

Answer 2

$log_{2}( log_{25}(5) ) \\ log_{2}( log_{ {5}^{2} }(5) ) \\ log_{2}( \frac{1}{2} log_{5}(5) ) \\ log_{2}( \frac{1}{2} ) \\ log_{2}( {2}^{ - 1} ) \\ - log_{2}(2) \\ - 1$
$\red{\boxed{Answer\:is\: -1}}$