Question

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

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

complete
\\(\log_{7}49 = 2\\)

complete
\\(\log_{7}98 \approx\\)

Explanation:

⚡ Using what you learned: properties of logarithms

Step 1: Identify the components

We are given:

$$ \log_{7} 98 = \log_{7} 2 + \log_{7} 49 $$

$$ \log_{7} 49 = 2 $$

From the top of the image, we can infer the given approximation:

$$ \log_{7} 2 \approx 0.356 $$

Step 2: Substitute and calculate

Substitute the known values into the expanded expression:

$$ \log_{7} 98 \approx 0.356 + 2 $$

$$ \log_{7} 98 \approx 2.356 $$

Answer:

2.356