25(3)^x = 2025

x=

1 answer

To solve the equation \( 25(3)^x = 2025 \), we first simplify the equation.

  1. Divide both sides by 25: \[ (3)^x = \frac{2025}{25} \]

  2. Calculate \( \frac{2025}{25} \): \[ \frac{2025}{25} = 81 \]

So the equation simplifies to: \[ (3)^x = 81 \]

  1. Next, express 81 as a power of 3: \[ 81 = 3^4 \]

  2. Now the equation is: \[ (3)^x = (3)^4 \]

  3. Since the bases are the same, we can set the exponents equal to each other: \[ x = 4 \]

Thus, the solution is: \[ \boxed{4} \]