Take the log to the base 3.
[tex]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}[/tex]
The appropriate choice is the first one ...
... -11/3
Question:
For what value of a does 9= (1/27)^a+3 ?
Answer: A
A. -11/3
B. -7/3
C. 7/3
D. 11/3
