Based on the estimates, we can conclude that [tex]\log _3(11)[/tex] is greater than [tex]\log_5 (20)[/tex].
To determine which of the two logarithms is greater, we can estimate what two numbers each log falls between.
Let's start with [tex]\log _3(11)[/tex],
Since 3² = 9 and 3³=27, we can estimate that [tex]\log _3(11)[/tex] is between 2 and 3.
Now let's consider [tex]\log_5 (20)[/tex],
Since 5² = 25 and 5³ = 125, we can estimate that [tex]\log_5 (20)[/tex] is between 1 and 2.
Therefore, based on our estimates, we can conclude that [tex]\log _3(11)[/tex] is greater than [tex]\log_5 (20)[/tex].
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