Question

evaluating logarithmic expressions 5.01 which logarithmic equation is equivalent to $3^2 = 9$? $2 = \log_{9} 3$ $2 = \log_{3} 9$ $3 = \log_{2} 9$ $3 = \log_{9} 2$

Explanation:

Step1: Recall the logarithmic definition

The definition of a logarithm is: if \(a^b = c\), then \(\log_a c = b\), where \(a>0,a
eq1\), \(c>0\).

Given the equation \(3^2 = 9\), here \(a = 3\), \(b = 2\), \(c=9\).

Step2: Apply the logarithmic definition

Using the definition \(\log_a c=b\) for \(a^b = c\), substituting \(a = 3\), \(b = 2\), \(c = 9\), we get \(\log_3 9=2\), which can be rewritten as \(2=\log_3 9\).

Answer:

\(2 = \log_{3}9\) (the second option among the given choices)