Answer:
TRUE
Step-by-step explanation:
Consider
[tex] log_{ \sqrt{x} }( {x}^{k} ) [/tex]
[tex] log_{ \sqrt{x} }( {( \sqrt{x} }^{2})^{k} ) [/tex]
[tex] log_{ \sqrt{x} }{( \sqrt{x})^{2k} } ) [/tex]
we know that
[tex] log( {a}^{b} ) = b log(a) [/tex]
===
[tex]2k (log_{ \sqrt{x} }( \sqrt{x} ) )[/tex]
Also we know that
[tex] log_{a}(a) = 1[/tex]
===
[tex]2k( log_{ \sqrt{x} }( \sqrt{x} ) = 2k \times 1 = 2k[/tex]
Hence
[tex] log_{ \sqrt{x} }( {x}^{k} ) = 2k[/tex]
Therefore it TRUE
