Question

properties of logarithms
given \\(\log_3 2 \approx 0.631\\) and \\(\log_3 7 \approx 1.771\\), what is \\(\log_3 14\\)?
1.118
1.893
3.542
2.402

Explanation:

Step1: Use logarithm product rule

Recall that \(\log_b(xy)=\log_b x+\log_b y\). So, \(\log_3 14=\log_3(2\times7)=\log_3 2+\log_3 7\).

Step2: Substitute given values

We know \(\log_3 2\approx0.631\) and \(\log_3 7\approx1.771\). Then, \(\log_3 14\approx0.631 + 1.771\).

Step3: Calculate the sum

\(0.631+1.771 = 2.402\).

Answer:

2.402