Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( n = 1 \)
Solution
To solve the equation \( 5^{3n} = 125 \) for \( n \), follow these steps:
1. **Recognize the Base Relationship:**
Notice that \( 125 \) is a power of \( 5 \). Specifically:
\[
125 = 5^3
\]
2. **Rewrite the Equation with Matching Bases:**
Substitute \( 125 \) with \( 5^3 \) in the original equation:
\[
5^{3n} = 5^3
\]
3. **Set the Exponents Equal:**
Since the bases are the same and the equation holds true, their exponents must be equal:
\[
3n = 3
\]
4. **Solve for \( n \):**
Divide both sides of the equation by \( 3 \):
\[
n = \frac{3}{3} \\
n = 1
\]
**Answer:** \( n = 1 \)
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Simplify this solution Mind Expander
To solve the equation \( 5^{3n} = 125 \), we can rewrite 125 as \( 5^3 \). This gives us \( 5^{3n} = 5^3 \). Since the bases are the same, we can set the exponents equal to each other, resulting in \( 3n = 3 \). Dividing both sides by 3, we find \( n = 1 \). To double-check our solution, we substitute \( n \) back into the original equation: \( 5^{3(1)} = 5^3 = 125 \), which is correct! So, \( n = 1 \) is indeed the solution.
