25(3)^x = 2025

Question

x=

Answer 1

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: \[ (3)^x = 81 \]

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

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

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

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