Question

which logarithmic equation is equivalent to 3² = 9?
2 = log₃9
2 = log₉3
3 = log₂9
3 = log₉2

Explanation:

Step1: Recall the logarithm - exponent conversion rule

The general rule is if \(a^b = c\), then \(b=\log_{a}c\), where \(a>0,a
eq1\), \(c > 0\).

Step2: Identify \(a\), \(b\), and \(c\) in the given equation \(3^2 = 9\)

Here, \(a = 3\), \(b = 2\), and \(c = 9\).

Step3: Convert to logarithmic form

Using the rule \(a^b = c\Rightarrow b=\log_{a}c\), we get \(2=\log_{3}9\).

Answer:

\(2=\log_{3}9\) (corresponding to the first - option in the multiple - choice list, assuming the first option was meant to be \(2 = \log_{3}9\) as there is a typo in the provided options)