To convert the exponential equation [tex]\(10^5 = 100,000\)[/tex] into a logarithmic equation, follow these steps:
1. Understand the Exponential Equation:
The given equation in exponential form is [tex]\(10^5 = 100,000\)[/tex]. This indicates that the base is 10, the exponent is 5, and the result (or the argument) of the exponentiation is 100,000.
2. Form the Logarithmic Equation:
In general, the exponential form [tex]\(b^e = a\)[/tex] can be transformed into the logarithmic form [tex]\(\log_b(a) = e\)[/tex], where [tex]\(b\)[/tex] is the base, [tex]\(a\)[/tex] is the argument, and [tex]\(e\)[/tex] is the exponent.
3. Apply the Values to the Formula:
Substituting the values from the exponential equation [tex]\(10^5 = 100,000\)[/tex],
- Base ([tex]\(b\)[/tex]) is 10
- Argument ([tex]\(a\)[/tex]) is 100,000
- Exponent ([tex]\(e\)[/tex]) is 5
The logarithmic form will be:
[tex]\[
\log_{10}(100,000) = 5
\][/tex]
4. Check for Understanding:
This means that the exponent 5 is the power to which the base 10 must be raised to yield the argument 100,000.
So, the exponential equation [tex]\(10^5 = 100,000\)[/tex] when converted into logarithmic form is:
[tex]\[
\log_{10}(100,000) = 5
\][/tex]
