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Problem 11

# Given that $$\log 3 \approx 0.4771$$ and $$\log 4 \approx$$ 0.6021, find the value of each logarithm. $$\log 12$$

Expert verified
The value of $$\log 12$$ is approximately 1.0792.
See the step by step solution

## Step 1: Express 12 as a product of 3 and 4

We can write the number 12 as the product of 3 and 4: $$12 = 3 \times 4$$

## Step 2: Apply logarithmic the product property

The logarithmic product property states that $$\log (ab) = \log a + \log b$$. Applying this property, we can write the logarithm of 12: $$\log 12 = \log (3 \times 4) = \log 3 + \log 4$$

## Step 3: Substitute the given values

Now, we can substitute the given values of $$\log 3$$ and $$\log 4$$ into the equation: $$\log 12 = 0.4771 + 0.6021$$

## Step 4: Calculate the sum

Now, we just need to calculate the sum: $$\log 12 \approx 0.4771 + 0.6021 = 1.0792$$ So, the value of $$\log 12$$ is approximately 1.0792.

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