Determine `f(0)` so that the function `f(x)` defined by `f(x)=((4^x-1)^3)/(sinx/4log(1+(x^2)/3))` becomes continuous at `x=0`

Explanation

To determine \( f(0) \) such that the function

\[ f(x) = \frac{(4^x - 1)^3}{\frac{\sin x}{4 \log(1 + \frac{x^2}{3})}} \]

is continuous at \( x = 0 \), we need to find the limit of \( f(x) \) as \( x \) approaches 0. For the function to be continuous at \( x = 0 \), we must have:

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