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