Question
What is the first step in proving that 10^log100 = 100
Solve for 10^x = 100
Deteirmen what log 100 is equal to
Divide both sides of the equation by 10
Cancel out the exponential base 10 and the logarithm
Solve for 10^x = 100
Deteirmen what log 100 is equal to
Divide both sides of the equation by 10
Cancel out the exponential base 10 and the logarithm
Answers
GPT-4o mini
To prove that \( 10^{\log 100} = 100 \), we can follow these steps:
1. **Determine what \( \log 100 \) is equal to**: Recall that \( \log 100 \) in base 10 is asking, "To what power must 10 be raised to get 100?" Since \( 100 = 10^2 \), we have:
\[
\log 100 = 2
\]
2. **Substitute back**: Now, substitute \( \log 100 \) back into the expression \( 10^{\log 100} \):
\[
10^{\log 100} = 10^2
\]
3. **Calculate \( 10^2 \)**:
\[
10^2 = 100
\]
Thus, we have demonstrated that \( 10^{\log 100} = 100 \).
In terms of the steps you provided, the appropriate first step for this proof would be:
**Determine what \( \log 100 \) is equal to.**
1. **Determine what \( \log 100 \) is equal to**: Recall that \( \log 100 \) in base 10 is asking, "To what power must 10 be raised to get 100?" Since \( 100 = 10^2 \), we have:
\[
\log 100 = 2
\]
2. **Substitute back**: Now, substitute \( \log 100 \) back into the expression \( 10^{\log 100} \):
\[
10^{\log 100} = 10^2
\]
3. **Calculate \( 10^2 \)**:
\[
10^2 = 100
\]
Thus, we have demonstrated that \( 10^{\log 100} = 100 \).
In terms of the steps you provided, the appropriate first step for this proof would be:
**Determine what \( \log 100 \) is equal to.**