Question

HELP!! Just need the answer to the question in the picture, please!

Answer 1

First thing to do is to switch the x and the y and then solve for the new y.  Easier said than done! Here's our equation with the switch: $x=2 ^{y} +6$.  We need to get that y out from inside that exponent.  This is an exponential equation, and the inverse of an exponential equation is a log equation.  Let's do some simplifying here first: $x-6=2 ^{y}$.  The 2 is now the base of our log (x-6) so now we have $y=log _{2} (x-6)$, which is the last choice above.