To solve the equation \( 25(3)^x = 2025 \), we first simplify the equation.
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Divide both sides by 25: \[ (3)^x = \frac{2025}{25} \]
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Calculate \( \frac{2025}{25} \): \[ \frac{2025}{25} = 81 \]
So the equation simplifies to: \[ (3)^x = 81 \]
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Next, express 81 as a power of 3: \[ 81 = 3^4 \]
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Now the equation is: \[ (3)^x = (3)^4 \]
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Since the bases are the same, we can set the exponents equal to each other: \[ x = 4 \]
Thus, the solution is: \[ \boxed{4} \]