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Answer :
To express the equation [tex]\(5^5 = 3125\)[/tex] in logarithmic form, follow these steps:
1. Identify the Components:
- The base of the exponentiation is [tex]\(5\)[/tex].
- The exponent is [tex]\(5\)[/tex].
- The result of the exponentiation is [tex]\(3125\)[/tex].
2. Understand Logarithmic Form:
- The expression [tex]\(b^a = c\)[/tex] can be written in logarithmic form as [tex]\(\log_b(c) = a\)[/tex].
- Here, [tex]\(b\)[/tex] is the base of the logarithm, [tex]\(c\)[/tex] is the result or the number you get when you raise the base [tex]\(b\)[/tex] to the power [tex]\(a\)[/tex], and [tex]\(a\)[/tex] is the exponent.
3. Apply the Components:
- Substitute [tex]\(b = 5\)[/tex], [tex]\(c = 3125\)[/tex], and [tex]\(a = 5\)[/tex] into the logarithmic form.
- This gives [tex]\(\log_5(3125) = 5\)[/tex].
So, the logarithmic form of the equation [tex]\(5^5 = 3125\)[/tex] is [tex]\(\log_5(3125) = 5\)[/tex].
1. Identify the Components:
- The base of the exponentiation is [tex]\(5\)[/tex].
- The exponent is [tex]\(5\)[/tex].
- The result of the exponentiation is [tex]\(3125\)[/tex].
2. Understand Logarithmic Form:
- The expression [tex]\(b^a = c\)[/tex] can be written in logarithmic form as [tex]\(\log_b(c) = a\)[/tex].
- Here, [tex]\(b\)[/tex] is the base of the logarithm, [tex]\(c\)[/tex] is the result or the number you get when you raise the base [tex]\(b\)[/tex] to the power [tex]\(a\)[/tex], and [tex]\(a\)[/tex] is the exponent.
3. Apply the Components:
- Substitute [tex]\(b = 5\)[/tex], [tex]\(c = 3125\)[/tex], and [tex]\(a = 5\)[/tex] into the logarithmic form.
- This gives [tex]\(\log_5(3125) = 5\)[/tex].
So, the logarithmic form of the equation [tex]\(5^5 = 3125\)[/tex] is [tex]\(\log_5(3125) = 5\)[/tex].
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