Question

Using log table evaluate 15.47*0.085^2/254^1÷3

Answer 1

To evaluate the expression \( \frac{15.47 \times 0.085^2}{254 \div 3} \) using logarithms, we'll follow these steps:

1. Calculate \( 0.085^2 \).
2. Calculate \( 254 \div 3 \).
3. Apply logarithms to the remaining multiplication and division.

### Step 1: Calculate \( 0.085^2 \)
\[
0.085^2 = 0.007225
\]

### Step 2: Calculate \( 254 \div 3 \)
\[
254 \div 3 = 84.6667 \quad (\text{approximately})
\]

### Step 3: Simplify the Expression
Now we can express the original expression using these calculations:
\[
\text{Expression} = \frac{15.47 \times 0.007225}{84.6667}
\]

### Step 4: Calculate the Logarithms
Using logarithm properties to compute the multiplication and division:
\[
\log \left( \frac{15.47 \times 0.007225}{84.6667} \right) = \log(15.47) + \log(0.007225) - \log(84.6667)
\]

Next, we will use logarithm tables for these values:

- Assume \( \log(15.47) \approx 1.189 \)
- Assume \( \log(0.007225) \approx -2.141 \)
- Assume \( \log(84.6667) \approx 1.928 \)

Now substituting:
\[
\log \left( \frac{15.47 \times 0.007225}{84.6667} \right) = 1.189 + (-2.141) - 1.928
\]
\[
= 1.189 - 2.141 - 1.928
\]
\[
= 1.189 - 4.069
\]
\[
\approx -2.880
\]

### Step 5: Get the Antilogarithm
Convert back to the original expression:
\[
\text{Value} \approx 10^{-2.880} \approx 0.001318
\]

So, the final result for the expression \( \frac{15.47 \times 0.085^2}{254 \div 3} \) is approximately:
\[
0.001318
\]