Question
Rewrite 45=1024 as a logarithmic equation.(1 point) Responses log45=1024 the log base 4 of 5 is equal to 1024 log51024=4 the log base 5 of 1024 is equal to 4 log10245=4 the log base 1024 of 5 is equal to 4 log41024=5 the log base 4 of 1024 is equal to 5
Answers
GPT-4o mini
To rewrite the equation \( 45 = 1024 \) in logarithmic form, you can use the relationship \( a = b^c \) which corresponds to \( \log_b(a) = c \).
However, given that \( 45 \) and \( 1024 \) do not have a direct base relationship, let's instead consider your options and rewrite pairs accordingly:
1. Start with the original statement and express it in terms of logs:
The equation can be interpreted as \( 1024 = 5^4 \).
Thus, it seems like the actual equation should relate to expressing \( 1024 \) in terms of its prime factors, as it is \( 4^5 \).
After checking the options, it looks like the closest aligned equation in logarithmic format would be:
- **log base 4 of 1024 is equal to 5**
So the correct logarithmic equation based on provided options would be:
\[
\log_{4}(1024) = 5
\]
Thus, that can be understood as confirming \( 1024 = 4^5 \) which verifies the logarithmic conversion with its basis.
However, given that \( 45 \) and \( 1024 \) do not have a direct base relationship, let's instead consider your options and rewrite pairs accordingly:
1. Start with the original statement and express it in terms of logs:
The equation can be interpreted as \( 1024 = 5^4 \).
Thus, it seems like the actual equation should relate to expressing \( 1024 \) in terms of its prime factors, as it is \( 4^5 \).
After checking the options, it looks like the closest aligned equation in logarithmic format would be:
- **log base 4 of 1024 is equal to 5**
So the correct logarithmic equation based on provided options would be:
\[
\log_{4}(1024) = 5
\]
Thus, that can be understood as confirming \( 1024 = 4^5 \) which verifies the logarithmic conversion with its basis.