Question

9=(1/27)^a+3 find a

-11/3
-7/3
7/3
11/3

Answer 1

To solve the equation 9 = (1/27)^a+3, we need to isolate the variable 'a'. The value of 'a' is -1.

Step-by-step explanation:

To solve the equation 9 = (1/27)^a+3, we need to isolate the variable 'a'.

Start by taking the logarithm of both sides of the equation. Using the logarithm property log(base a) (a^n) = n, we can rewrite the equation as:

log(base 1/27) 9 = a + 3

Since log(base 1/27) 9 is the exponent to which (1/27) must be raised to get 9, we can rewrite the equation as:

(1/27)^(a+3) = 9

Now, we need to express both sides of the equation with the same base. Rewrite 9 as (1/27)^(a+3) using exponent rules:

(1/27)^(a+3) = (1/27)^2

Since the bases are now the same, the exponents must be equal:

a + 3 = 2

Subtracting 3 from both sides gives us the value of 'a':

a = 2 - 3

a = -1

Answer 2

Step-by-step explanation:

I think you made some mistakes in the problem definition.

I guess you mean

9 = (1/27)^(a+3)

let's think about how to create 9 out of 1/27 just by using exponents.

we note that 27 is 3³. and therefore the cubic root of 27 is 3.

so,

(1/27)^(1/3) = 1/3

because the exponent 1/3 means "cubic root". an exponent 1/2 means square root. and so on.

making the exponent negative means 1/...

so,

(1/27)^(-1/3) = 3

and now, with what exponent operation can we turn 3 into 9 ?

by squaring it.

so,

((1/27)^(-1/3))² = 9

putting an exponent on an exponent means to multiply the exponents during simplification.

therefore,

((1/27)^(-1/3))² = (1/27)^(-2/3) = 9

that means

a + 3 = -2/3

a = -2/3 - 3 = -2/3 - 9/3 = -11/3

so, the first answer option is correct.