Question

True or false? Show steps

Answer 1

TRUE

Explanation:

Consider

`log_( √(x) )( {x}^(k) )`

`log_( √(x) )( {( √(x) }^(2))^(k) )`

`log_( √(x) ){( √(x))^(2k) } )`

we know that

`log( {a}^(b) ) = b log(a)`

===

`2k (log_( √(x) )( √(x) ) )`

Also we know that

`log_(a)(a) = 1`

===

`2k( log_( √(x) )( √(x) ) = 2k * 1 = 2k`

Hence

`log_( √(x) )( {x}^(k) ) = 2k`

Therefore it TRUE