Question

for what value of (x) does (3^{2x} = 9^{3x-4})?

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Explanation:

⚡ Using what you learned: Solving Exponential Equations

Step 1: Express with a common base

$$ 3^{2x} = (3^2)^{3x-4} $$

$$ 3^{2x} = 3^{2(3x-4)} $$

Step 2: Equate exponents and solve

$$ 2x = 2(3x-4) $$

$$ 2x = 6x - 8 $$

$$ -4x = -8 $$

$$ x = 2 $$

Answer:

2