Question

For what value of a does 9= (1/27)^a+3 ? -11/3 -7/3 7/3 11/3

Answer 1

Take the log to the base 3.

$9=\left(\dfrac{1}{27}\right)^{a+3}\\\\3^{2}=\left(3^{-3}\right)^{(a+3)}\\\\2=-3(a+3)\quad\text{base 3 log; equates exponents of 3}\\\\-\dfrac{2}{3}=a+3\quad\text{divide by -3}\\\\-\dfrac{11}{3}=a\quad\text{add -3}$

The appropriate choice is the first one ...

... -11/3