The mean lives of a radioactive substance are 1620 years and 405 years for `alpha` emission and `beta` emission respectively. Find out the time during which three fourth of a sample will decay if it is decaying both by `alpha`-emission and `beta`-emission simultaneously. `(log_e4=1.386).`

Explanation

To solve the problem, we need to find the time during which three-fourths of a radioactive sample will decay when it is decaying through both alpha and beta emissions simultaneously. We will follow these steps:

### Step 1: Calculate the decay constants for alpha and beta emissions.

The mean life (τ) is related to the decay constant (λ) by the formula:
\[ \lambda = \frac{1}{\tau} \]
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