To determine the logarithmic equation equivalent to the exponential equation \( 9^x = 27 \), we can follow the general properties of logarithms.
When dealing with an exponential equation of the form \( a^b = c \), it can be transformed into a logarithmic equation as \( b = \log_a(c) \).
Here, our equation is \( 9^x = 27 \).
We want to rewrite this in logarithmic form. According to the property, we should set:
[tex]\[ x = \log_9(27) \][/tex]
Therefore, the equivalent logarithmic equation is:
[tex]\[ x = \log_9(27) \][/tex]
So, the correct answer is:
B. [tex]\( x = \log_9 27 \)[/tex]
