Question

complete the steps to evaluate \\(\log_{7}98\\), given \\(\log_{7}2 \approx 0.356\\).

how can you rewrite \\(\log_{7}98\\) using the product property?

\\(\bigcirc\\) \\(7\log 2 + 7\log 49\\)
\\(\bigcirc\\) \\(\log 7 + \log 2 + \log 49\\)
\\(\bigcirc\\) \\(\log_{7}2 + \log_{7}49\\)

Explanation:

⚡ Using what you learned: properties of logarithms

Step 1: Identify factors of the argument

To rewrite \(\log_{7}98\) using the product property, express the number \(98\) as a product of factors, specifically using the base \(7\) and the given value's argument \(2\):

$$98 = 2 \times 49$$

Step 2: Apply the product property of logarithms

The product property of logarithms states that:

$$\log_{b}(x \cdot y) = \log_{b}x + \log_{b}y$$

Substitute \(2\) and \(49\) into the property with base \(7\):

$$\log_{7}(2 \cdot 49) = \log_{7}2 + \log_{7}49$$

Answer:

\(\log_{7}2 + \log_{7}49\)