Question
What is the first step in proving that 10log¹⁰⁰=100
?(1 point)
Responses
Divide both sides of the equation by 10.
Determine what logarithm 100 is equal to.
Cancel out the exponential base 10 and the logarithm.
Solve the equation 10x=100
?(1 point)
Responses
Divide both sides of the equation by 10.
Determine what logarithm 100 is equal to.
Cancel out the exponential base 10 and the logarithm.
Solve the equation 10x=100
Answers
GPT-4o mini
To prove that \( 10 \log_{10} 100 = 100 \), the first step is to **determine what the logarithm \( 100 \) is equal to**.
This means calculating \( \log_{10} 100 \), which gives us the exponent that 10 must be raised to in order to equal 100. Since \( 10^2 = 100 \), we find that \( \log_{10} 100 = 2 \). Then we can proceed to substitute this value back into the equation.
So, the correct response is:
**Determine what logarithm \( 100 \) is equal to.**
This means calculating \( \log_{10} 100 \), which gives us the exponent that 10 must be raised to in order to equal 100. Since \( 10^2 = 100 \), we find that \( \log_{10} 100 = 2 \). Then we can proceed to substitute this value back into the equation.
So, the correct response is:
**Determine what logarithm \( 100 \) is equal to.**