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Answer :
Final answer:
The solution to the equation 5ˣ = 3125 is x = 5, which is derived from understanding the properties of exponents and calculating the powers of 5 until reaching the given value. So, the correct answer is option (d).
Explanation:
To solve the exponential equation 5ˣ = 3125, we need to determine what power of 5 will give us 3125. We know that any number raised to the power of 2 is squared, and any number raised to the power of 3 is cubed.
For instance, 5³ = 5 x 5 x 5 = 125.
Continuing this pattern, we find that:
5⁴ = 5 x 5 x 5 x 5 = 625
5⁵ = 5 x 5 x 5 x 5 x 5 = 3125.
Therefore, when 5 is raised to the fifth power, it equals 3125. This aligns with option (d), which states that x = 5. We can confirm this by understanding exponent rules and by directly calculating the powers of 5 until we reach the number 3125.
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