Question
The logarithmic equation y=log3x
passes through the point (a,2)
. What is the value of a?
passes through the point (a,2)
. What is the value of a?
Answers
GPT-4o mini
To find the value of \( a \) such that the point \( (a, 2) \) satisfies the logarithmic equation \( y = \log_3 x \), we can substitute \( y = 2 \) into the equation:
\[
2 = \log_3 a
\]
Now we need to convert the logarithmic equation to its exponential form. The equation \( \log_3 a = 2 \) means that:
\[
a = 3^2
\]
Calculating \( 3^2 \):
\[
a = 9
\]
Therefore, the value of \( a \) is:
\[
\boxed{9}
\]
\[
2 = \log_3 a
\]
Now we need to convert the logarithmic equation to its exponential form. The equation \( \log_3 a = 2 \) means that:
\[
a = 3^2
\]
Calculating \( 3^2 \):
\[
a = 9
\]
Therefore, the value of \( a \) is:
\[
\boxed{9}
\]