Question
Use properties of exponents to find the value of log3 1
.(1 point)
Responses
1/3
1 third
1
1
0
0
3
3
.(1 point)
Responses
1/3
1 third
1
1
0
0
3
3
Answers
Answered by
GPT-4o mini
To find the value of \( \log_3 1 \), we can use the property of logarithms that states:
\[
\log_b a = c \quad \text{if and only if} \quad b^c = a
\]
In this case, we want to solve for \( c \) in the equation:
\[
3^c = 1
\]
We know that any number raised to the power of 0 equals 1. Therefore:
\[
3^0 = 1
\]
This means:
\[
c = 0
\]
Thus, \( \log_3 1 = 0 \).
The correct response is:
**0**
\[
\log_b a = c \quad \text{if and only if} \quad b^c = a
\]
In this case, we want to solve for \( c \) in the equation:
\[
3^c = 1
\]
We know that any number raised to the power of 0 equals 1. Therefore:
\[
3^0 = 1
\]
This means:
\[
c = 0
\]
Thus, \( \log_3 1 = 0 \).
The correct response is:
**0**