What value of n solves the equation?

3^n = 1/81

A.
–243

B.
–27

C.
–4

D.
4

Question

What value of n solves the equation? 
 
3^n = 1/81
 
 A.
–243
 
 B.
–27
 
 C.
–4
 
 D.
4

mathstudent55 · Answer

Can you write 81 as a power of 3?

anonymous · Answer

I honestly don't know, mathstudent55.

anonymous · Answer

Could you tell me how?

mathstudent55 · Answer

$3^1 = 3$

$3^2 = 3 \times 3 = 9$

$3^3 = 3 \times 3 \times 3 = 27$

$3^4 = 3 \times 3 \times 3 \times 3 = 81$

Do you see that $81 = 3^4$  ?

anonymous · Answer

Yes.

anonymous · Answer

I get it now.

mathstudent55 · Answer

Now look at the right side of the original problem.

You have $\dfrac{1}{81} $

Since we now know that $81 = 3^4$, we can rewrite the right siuda as

$\dfrac{1}{81} = \dfrac{1}{3^4} $

anonymous · Answer

Okay.

mathstudent55 · Answer

The question now is:

$3^n = \dfrac{1}{3^4} $

Now we use the definition of a negative exponent:

$a^{-n} = \dfrac{1}{a^n} $

mathstudent55 · Answer

We start from the right side of the definition:

$\dfrac{1}{a^n} = a^{-n} $

If we use the fraction from your problem, and we follow the definition, we get:

$\dfrac{1}{3^4} = 3^{-4} $

mathstudent55 · Answer

The exponent, n, is -4.
Answer: C. -4

anonymous · Answer

I get it now. Thanks!