Question

Find x, if : `sqrt( 2^( x + 3 )) = 16`

Answer 1

`sqrt( 2^( x + 3 )) = 16`

`( 2^( x + 3 ))^(1/2) = 2 xx 2 xx 2 xx 2`

⇒ `( 2 )^[(x + 3)/2] = 2^4`

We know that if bases are equal, the powers are equal.
⇒ `[ x + 3 ]/2 = 4`

⇒ x + 3 = 8
⇒ x = 8 - 3
⇒ x = 5