Question

Solve the log of 9.23 multiply by 0.00921 divide by 0.05138
Using logarithms of number less than 1

Answer 1

To solve the expression involving logarithms, we can break it down step by step. We need to compute:

\[
\log(9.23) + \log(0.00921) - \log(0.05138)
\]

### Step 1: Calculate the logs

1. **Calculate \(\log(9.23)\)**:
- We can use a calculator or logarithm tables to find this value.
- \(\log(9.23) \approx 0.965\)

2. **Calculate \(\log(0.00921)\)**:
- Since \(0.00921 = 9.21 \times 10^{-3}\):
- \(\log(0.00921) = \log(9.21) + \log(10^{-3}) = \log(9.21) - 3\)
- \(\log(9.21) \approx 0.965\) (from the previous calculation)
- Thus, \(\log(0.00921) \approx 0.965 - 3 = -2.035\)

3. **Calculate \(\log(0.05138)\)**:
- Since \(0.05138 = 5.138 \times 10^{-2}\):
- \(\log(0.05138) = \log(5.138) + \log(10^{-2}) = \log(5.138) - 2\)
- \(\log(5.138) \approx 0.712\)
- Thus, \(\log(0.05138) \approx 0.712 - 2 = -1.288\)

### Step 2: Substitute values into the main equation

Now substitute the calculated values back into the original equation:

\[
\log(9.23) + \log(0.00921) - \log(0.05138)
\]

Substituting our values, we get:

\[
0.965 + (-2.035) - (-1.288) = 0.965 - 2.035 + 1.288
\]

### Step 3: Calculate the result

Calculating the above:

1. \(0.965 - 2.035 = -1.07\)
2. Now add \(1.288\):

\(-1.07 + 1.288 = 0.218\)

### Final Answer:

Thus, the value of \(\log(9.23 \times 0.00921 / 0.05138)\) is approximately \(0.218\).