An organic compound undergoes first decompoistion. The time taken for its decompoistion to `1//8` and `1//10` of its initial concentration are `t_(1//8)` and `t_(1//10)`, respectively. What is the value of `([t_(1//8)])/([t_(1//10)]) xx 10`? `(log_(10)2 = 0.3)`

Explanation

To solve the problem, we need to find the ratio of the times taken for the decomposition of an organic compound to \( \frac{1}{8} \) and \( \frac{1}{10} \) of its initial concentration, and then multiply that ratio by 10.

### Step-by-Step Solution:

1. **Understanding the Reaction**: The organic compound undergoes a first-order decomposition reaction. For a first-order reaction, the time taken for a certain fraction of the reactant to decompose can be calculated using the formula:
\[ t = \frac{2.303}{k} \log \left( \frac{[A_0]}{[A]} \right) \]
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