Find the value of `(23.17)^((1)/(5.76))` using log table.

Answer

To find the value of \( (23.17)^{\frac{1}{5.76}} \) using logarithms, we can follow these steps:

### Step 1: Set up the equation
Let \( y = (23.17)^{\frac{1}{5.76}} \).

### Step 2: Take logarithm on both sides
Taking logarithm (base 10) on both sides, we have:
\[ \log y = \log \left( (23.17)^{\frac{1}{5.76}} \right) \]

### Step 3: Apply the power rule of logarithms
Using the power rule of logarithms, we can rewrite the equation as:
\[ \log y = \frac{1}{5.76} \log (23.17) \]

### Step 4: Find \( \log (23.17) \) using the log table
From the log table, we find:
\[ \log (23.17) \approx 1.3649 \]

### Step 5: Substitute the value of \( \log (23.17) \)
Now substituting this value into our equation:
\[ \log y = \frac{1.3649}{5.76} \]

### Step 6: Calculate \( \frac{1.3649}{5.76} \)
Now we perform the division:
\[ \log y \approx 0.2370 \]

### Step 7: Find the antilogarithm
To find \( y \), we need to calculate the antilogarithm of \( \log y \):
\[ y = 10^{0.2370} \]

### Step 8: Calculate \( 10^{0.2370} \)
Using the antilog table or calculator, we find:
\[ y \approx 1.7257 \]

### Final Answer
Thus, the value of \( (23.17)^{\frac{1}{5.76}} \) is approximately \( 1.7257 \).

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