Question

What is the value of x? (1/3)^x-2 =(1/3)^2

Answer 1

Answer:

Step-by-step explanation:

Hi there,

To solve this, we want to isolate x either using logs or exponent rules. For this, I chose exponent rules.

First, divide both sides of the equation by (1/3)² :

$\frac{((\frac{1}{3} )^{x-2} )}{(\frac{1}{3} )^{2} } = \frac{(\frac{1}{3} )^{2} }{(\frac{1}{3} )^{2} }$

The right-hand side is reduced to 1. The left-hand side contains values that have the same base, so we can use this exponent rule:

$\frac{x^{a} }{x^{b} } =x^{a-b}$ Apply this:

$(\frac{1}{3})^{x-2-2}=(\frac{1}{3})^{x-4}=1$     Now, we are left with:

$(\frac{1}{3})^{x-4}=1$    

Conceptually, you just have to think: what exponent can make a base equal to 1?

This is based on the following exponent rule:

$x^{0} =1$

So, all we have to do is set (x-4) = 0!

$x-4=0\\x=4$

Thus, the value of x is 4.

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