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Problem 12

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

Expert verified
The value of $$\log \frac{3}{4}$$ is approximately $$-0.1250$$.
See the step by step solution

## Step 1: Use logarithmic property to rewrite given expression

We can rewrite the given logarithm using the logarithmic property as: $$\log \frac{3}{4} = \log 3 - \log 4$$

## Step 2: Substitute the given values

Replace the given approximations for $$\log3$$ and $$\log4$$ in the expression: $$\log \frac{3}{4} = 0.4771 - 0.6021$$

## Step 3: Perform the calculation

Subtract the values of $$\log 3$$ and $$\log 4$$ to find the value of $$\log \frac{3}{4}$$: $$\log \frac{3}{4} \approx -0.1250$$ So, the value of $$\log \frac{3}{4}$$ is approximately $$-0.1250$$.

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