Question
25(3)^x = 2025
x=
x=
Answers
GPT-4o mini
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:
\[
\boxed{4}
\]
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:
\[
\boxed{4}
\]