[tex] {3}^{x} - {3}^{x - 2} = 72[/tex]

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To solve this equation, we can first simplify the expression on the left side of the equation.

[tex] {3}^{x} - {3}^{x - 2} [/tex
[tex] = {3}^{x} - \frac{{3}^{x}}{{3}^{2}} [/tex
[tex] = {3}^{x} - \frac{{3}^{x}}{{9}} [/tex
[tex] = {3}^{x} - \frac{1}{9}{3}^{x} [/tex
[tex] = \frac{9}{9}{3}^{x} - \frac{1}{9}{3}^{x} [/tex
[tex] = \frac{8}{9}{3}^{x} [/tex]

So, the equation becomes:

[tex] \frac{8}{9}{3}^{x} = 72 [/tex]

Next, we can simplify this equation by multiplying both sides by 9:

[tex] 8{3}^{x} = 72 \times 9 [/tex
[tex] 8{3}^{x} = 648 [/tex]

Now, we can rewrite 648 as a power of 3:

648 = 3^4 * 2

So, the equation becomes:

[tex] 8{3}^{x} = {3}^{4} \times 3^{2} [/tex]

Then, by using the property of exponents (a^m * a^n = a^(m + n)), we have:

[tex] 8{3}^{x} = {3}^{x + 6} [/tex]

Equating the exponents, we get:

x + 6 = x

This is not possible, so there might be a mistake in the calculation. Let's start from the beginning and see if there was an error.