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 :
[tex]\frac{((\frac{1}{3} )^{x-2} )}{(\frac{1}{3} )^{2} } = \frac{(\frac{1}{3} )^{2} }{(\frac{1}{3} )^{2} } \\[/tex]
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:
[tex]\frac{x^{a} }{x^{b} } =x^{a-b}[/tex] Apply this:
[tex](\frac{1}{3})^{x-2-2}=(\frac{1}{3})^{x-4}=1[/tex] Now, we are left with:
[tex](\frac{1}{3})^{x-4}=1[/tex]
Conceptually, you just have to think: what exponent can make a base equal to 1?
This is based on the following exponent rule:
[tex]x^{0} =1[/tex]
So, all we have to do is set (x-4) = 0!
[tex]x-4=0\\x=4[/tex]
Thus, the value of x is 4.
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