Problem Solving (PS) | Re: If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?

We can simplify the given equation:

3^a - (3^a)(3^-2) = 8(3^27)

Factor 3^a from the left side:

3^a(1 - 1/9) = 8(3^27)

3^a(8/9) = 8(3^27)

3^a = 8(3^27) x 9/8

3^a = 3^27 x 3^2

3^a = 2^29

a = 29

So, 2a = 58.

Alternate Solution:

Observe that 3^a = 3^(a - 2 + 2) = (3^(a - 2))(3^2). Then:

(3^(a - 2))(3^2) - (3^(a - 2)) = 8(3^27)

Let’s factor the common 3^(a - 2) from the left
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