Question

given \\(\log_{3} 2 \approx 0.631\\) and \\(\log_{3} 7 \approx 1.771\\), what is \\(\log_{3} 14\\)?

\\(\bigcirc\\) 1.118
\\(\bigcirc\\) 1.893
\\(\bigcirc\\) 2.402
\\(\bigcirc\\) 3.542

Explanation:

⚡ Using what you learned: properties of logarithms

Step 1: Apply the Product Rule

$$ \log_{3}(14) = \log_{3}(2 \times 7) = \log_{3}(2) + \log_{3}(7) $$

Step 2: Substitute and Calculate

$$ \log_{3}(14) \approx 0.631 + 1.771 = 2.402 $$

Answer:

2.402