EVALUATE USING LOG TABLE
`(0.9876 xx (16.42)^(2))/((4.567)^(1/3))`

Answer

To evaluate the expression \((0.9876 \times (16.42)^{2}) / ((4.567)^{1/3})\) using logarithms, we can follow these steps:

### Step 1: Write the expression in logarithmic form
Let \( x = \frac{0.9876 \times (16.42)^{2}}{(4.567)^{1/3}} \).

### Step 2: Apply logarithmic properties
Taking logarithm on both sides, we have:
\[ \log x = \log(0.9876 \times (16.42)^{2}) - \log((4.567)^{1/3}) \]

### Step 3: Use the properties of logarithms
Using the properties of logarithms:
- \(\log(a \times b) = \log a + \log b\)
- \(\log(a^{n}) = n \cdot \log a\)

We can rewrite the equation as:
\[ \log x = \log(0.9876) + \log((16.42)^{2}) - \log((4.567)^{1/3}) \]
\[ \log x = \log(0.9876) + 2 \cdot \log(16.42) - \frac{1}{3} \cdot \log(4.567) \]

### Step 4: Look up logarithm values
Using a logarithm table, we find:
- \(\log(0.9876) \approx -0.0054\)
- \(\log(16.42) \approx 1.2152\)
- \(\log(4.567) \approx 0.6600\)

### Step 5: Substitute the values into the equation
Substituting the logarithm values:
\[ \log x = -0.0054 + 2 \cdot 1.2152 - \frac{1}{3} \cdot 0.6600 \]

### Step 6: Calculate each term
Calculating the terms:
- \(2 \cdot 1.2152 = 2.4304\)
- \(\frac{1}{3} \cdot 0.6600 \approx 0.2200\)

### Step 7: Combine the results
Now, substituting back:
\[ \log x = -0.0054 + 2.4304 - 0.2200 \]
\[ \log x = 2.2050 \]

### Step 8: Find the antilogarithm
To find \( x \), we take the antilogarithm:
\[ x = 10^{2.2050} \]

### Step 9: Calculate the final value
Using a calculator:
\[ x \approx 126.4 \]

Thus, the evaluated value of the expression \((0.9876 \times (16.42)^{2}) / ((4.567)^{1/3})\) is approximately **126.4**.

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