Question
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Tutor-Verified Answer
Answer
\( x = 5 \)
Solution
We start with the equation:
3^x = 243
Notice that 243 is a power of 3. In fact:
3^5 = 243
Thus, we can rewrite the equation as:
3^x = 3^5
Since the bases are the same, the exponents must be equal:
x = 5
So, the solution is x = 5.
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Simplify this solution Bonus Knowledge
To solve the equation \( 3^{x} = 243 \), we can rewrite 243 as a power of 3. Since \( 243 = 3^5 \), we can substitute that into the equation: \[ 3^{x} = 3^5 \] Now, since the bases are the same, we can set the exponents equal to each other: \[ x = 5 \] So, the solution to the equation is \( x = 5 \). If you ever get stuck with exponential equations, try transforming the numbers into powers of the same base. It can make problem-solving as smooth as butter!
