Question
what is the logarithmic version of 1=3^0
Answers
GPT-4o mini
To express the equation \( 1 = 3^0 \) in logarithmic form, we start with the fact that the expression \( 3^0 = 1 \) can be rewritten using logarithms.
The general form for converting an exponential equation \( a^b = c \) into logarithmic form is:
\[
\log_a(c) = b
\]
In this case, we can identify \( a = 3 \), \( b = 0 \), and \( c = 1 \). Thus, we can rewrite \( 1 = 3^0 \) in logarithmic form as:
\[
\log_3(1) = 0
\]
This means that the logarithm base 3 of 1 is equal to 0, confirming that \( 3^0 = 1 \).
The general form for converting an exponential equation \( a^b = c \) into logarithmic form is:
\[
\log_a(c) = b
\]
In this case, we can identify \( a = 3 \), \( b = 0 \), and \( c = 1 \). Thus, we can rewrite \( 1 = 3^0 \) in logarithmic form as:
\[
\log_3(1) = 0
\]
This means that the logarithm base 3 of 1 is equal to 0, confirming that \( 3^0 = 1 \).