Evaluate [tex]\log_{9} 27[/tex]. Can someone explain this to me so I can do similar tasks on my own?
Answer (3)
l o g 9 27 = l o g 9 3 3 = 3 l o g 9 3 = 3 l o g 9 9 = 3 l o g 9 9 2 1 = 2 1 ⋅ 3 l o g 9 9 = 2 3
You would use some properties of the logarithm. First, l o g 9 27 = l o g 3 2 27 = 2 1 l o g 3 27 . So, now you have l o g 3 27 to calculate. It's l o g 3 3 3 = 3 , so the final result is 2 1 ∗ 3 = 2 3 Hope it helps.
To find \( \log_{9} 27 \), we express 27 as 3^3 \ and use properties of logarithms. We convert the base to simplify, finding that ( \log_{9} 3 = \frac{1}{2} \, giving us \log_{9} 27 = \frac{3}{2}.
;
