Question

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

Answer 1

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

Answer 2

Take the log to the base 3.

`9=\left((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}\\\\-(2)/(3)=a+3\quad\text{divide by -3}\\\\-(11)/(3)=a\quad\text{add -3}`

The appropriate choice is the first one ...

... -11/3