Question

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

Answer 1

Answer:

Answer: a=-11/3 or a=-3.667 (approx.)

Step-by-step explanation:

Answer 2

Given: 9=(1/27)^(a+3)

[Note:  Please review rules of PEMDAS.  
The question posted as is means
9=[(1/27)^a]+3 which is probably not what you mean.  It has been interpreted with (a+3) as the exponent, please check.]

Need to find value of a that satisfies above.

We will first isolate a in order to solve for its value.
9=(1/27)^(a+3)
Switch unknown to the left
(1/27)^(a+3) = 9
Since both 27 and 9 are powers of 3, we can take log to base 3.
take log (base 3) on both sides, applying rule of logarithm of exponents.
(a+3)log_3(1/27)=log_3(9)
(a+3)log_3(3^(-3))=log_3(3^2)
Apply definition of logarithm [log_a(a^k)=k]
(a+3)(-3)=2
(a+3)=-2/3
a=-3 2/3=-11/3

Check: (1/27)^(-11/3+3)=(1/27)^(-2/3)=(3^(-3))^(-2/3)=3^(-3(-2/3))=3^2=9 ok

Answer: a=-11/3 or a=-3.667 (approx.)