In mathematics, what is the exact solution to the exponential equation $4 \cdot e^{2 x} = 28$ ?

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In mathematics, what is the vertex of the parabola defined by the quadratic function $f (x) = x^{2} - 6 x + 8$ ?
In mathematics, what is the doubling time $T_{2}$ for the exponential growth model $f (x) = 150 \cdot 1.0 5^{x}$ ?
In mathematics, what is the half-life $T_{1/2}$ of a decaying substance modeled by $N (t) = 800 \cdot 0.8 5^{t}$ ?
In mathematics, if a power function $f (x) = b \cdot x^{a}$ passes through $(1, 4)$ and $(2, 32)$ , what is the exponent $a$ ?
In mathematics, what is the domain of the real logarithmic function $f (x) = ln (3 x - 12)$ ?
In mathematics, what is the discriminant $d$ of the quadratic equation $2 x^{2} - 5 x + 3 = 0$ and how many real roots exist?