Optimizied Simplifying Log798 Using the Product Property and Sum Property of Logarithms

Complete the steps to evaluate log798, given log72 ≈ 0.356.How can you rewrite log798 using the product property?

To rewrite log798 using the product property, we can utilize the fact that log(a * b) can be expressed as the sum of log(a) and log(b)

To rewrite log798 using the product property, we can utilize the fact that log(a * b) can be expressed as the sum of log(a) and log(b).

Step 1: Rewrite 798 as a product of smaller numbers
We can rewrite 798 as 72 * 11.

Step 2: Express log798 using the product property
Using the product property, we can rewrite log798 as log(72 * 11).

Step 3: Apply the sum property of logarithms
Since 72 is already given to us as log72, we can rewrite log(72 * 11) as log72 + log11.

Step 4: Substitute the given value
Given that log72 ≈ 0.356, we can substitute it into the expression from step 3 to obtain:
log(72 * 11) ≈ 0.356 + log11.

Therefore, log798 can be rewritten using the product property as 0.356 + log11.

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