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Bunuel
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Equate 3 power in both sides
2(2-x)=x-1
x=5/3
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Bunuel
If \(9^{(2 − x)} = 3^{(x − 1)}\), what is the value of x?

A. 3
B. 5
C. 5/2
D. 5/3
E. 3/5

\(9^{(2 − x)} = 3^{(x − 1)}\)

Or, \(3^{2(2 − x)} = 3^{(x − 1)}\)

Or, \(4 - 2x = x - 1\)

Or, \(3x = 5\)

So, \(x = \frac{5}{3}\)

Thus, answer will be (D) \(x = \frac{5}{3}\)
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Bunuel
If \(9^{(2 − x)} = 3^{(x − 1)}\), what is the value of x?

A. 3
B. 5
C. 5/2
D. 5/3
E. 3/5

When we have an exponential equation, if the bases are the same, then we can equate the exponents. In the given equation, we must express 9 as 3^2 to make the bases the same. We can simplify the given equation:

9^(2-x) = 3^(x-1)

3^2(2-x) = 3^(x-1)

3^(4-2x) = 3^(x-1)

4 - 2x = x - 1

5 = 3x

5/3 = x

Answer: D
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