9^x=1/3

How much is x?

x = -1/2

Step-by-step explanation:

This question can be solved by applying the laws of indices

In a^n, a - base

n - index

Given

9^x = 1/3

According to the laws of indices, a/b = b^(-a)

Hence we can write, 1/3 = 3^(-1)

9^x = 3^(2x)

Again according to the laws of indices,

a^b = a^n can be written as;

b = n

That is, if in an equation the bases are the same, the indices are also equal.

So we can write,

3^(2x) = 3^(-1)

2x = -1

Divide both sides of the equation by 2, the coefficient of x

2x/2 = -1/2

x = -1/2

All of the following are equivalent except for 0.4. the first choice has a value of 4% which when converted to its decimal equivalent is 0.04. this was obtained by dividing the percent value by 100. the value 0.4 is actually equivalent to 40% and not 4%. this makes it the odd value out of the three choices.