Question

if \\(\log 3 \approx 0.48\\) and \\(\log 6 \approx 0.78\\), then what is the approximate value of \\(\log 18\\)? leave 4 decimal places in your answer. (20 points)\\(\log 18 \approx \square\\)

Explanation:

Step1: Recall log property (product rule)

The logarithm of a product is the sum of the logarithms, i.e., \(\log(ab)=\log a+\log b\). Notice that \(18 = 3\times6\), so \(\log 18=\log(3\times6)\).

Step2: Apply the product rule

Using the product rule \(\log(3\times6)=\log 3+\log 6\). We know that \(\log 3\approx0.48\) and \(\log 6\approx0.78\).

Step3: Calculate the sum

Substitute the given values: \(0.48 + 0.78=1.26\). Since we need to leave 4 decimal places, we can write it as \(1.2600\).

Answer:

\(1.2600\)