Answer :
To write the equation [tex]\(5^5 = 3125\)[/tex] in logarithmic form, we need to understand the relationship between exponents and logarithms.
In general, the expression [tex]\(b^c = a\)[/tex] can be converted into its logarithmic form as [tex]\(\log_b(a) = c\)[/tex]. Here:
- [tex]\(b\)[/tex] is the base of the exponential expression.
- [tex]\(a\)[/tex] is the result.
- [tex]\(c\)[/tex] is the exponent.
Now, let's apply this to your specific equation:
1. Identify the base, the result, and the exponent in the equation [tex]\(5^5 = 3125\)[/tex]:
- The base ([tex]\(b\)[/tex]) is 5.
- The result ([tex]\(a\)[/tex]) is 3125.
- The exponent ([tex]\(c\)[/tex]) is 5.
2. Convert this into logarithmic form using the relationship [tex]\(\log_b(a) = c\)[/tex]:
- Here, [tex]\(b = 5\)[/tex], [tex]\(a = 3125\)[/tex], and [tex]\(c = 5\)[/tex].
Thus, the logarithmic form of the equation [tex]\(5^5 = 3125\)[/tex] is:
[tex]\[
\log_5(3125) = 5
\][/tex]
This means that the exponent we would raise the base 5 to, in order to get 3125, is 5.
In general, the expression [tex]\(b^c = a\)[/tex] can be converted into its logarithmic form as [tex]\(\log_b(a) = c\)[/tex]. Here:
- [tex]\(b\)[/tex] is the base of the exponential expression.
- [tex]\(a\)[/tex] is the result.
- [tex]\(c\)[/tex] is the exponent.
Now, let's apply this to your specific equation:
1. Identify the base, the result, and the exponent in the equation [tex]\(5^5 = 3125\)[/tex]:
- The base ([tex]\(b\)[/tex]) is 5.
- The result ([tex]\(a\)[/tex]) is 3125.
- The exponent ([tex]\(c\)[/tex]) is 5.
2. Convert this into logarithmic form using the relationship [tex]\(\log_b(a) = c\)[/tex]:
- Here, [tex]\(b = 5\)[/tex], [tex]\(a = 3125\)[/tex], and [tex]\(c = 5\)[/tex].
Thus, the logarithmic form of the equation [tex]\(5^5 = 3125\)[/tex] is:
[tex]\[
\log_5(3125) = 5
\][/tex]
This means that the exponent we would raise the base 5 to, in order to get 3125, is 5.
