Determine the exact value of a that satisfies the equation 5(2" ) = 3(74-4). Enter log (a) as log(a). Include brackets around the numerator and denominator. For example, (log(2)+log(5))/(3log(4)). TThe graph of the function f(@) = 4" was reflected and then translated. As a result, the new function is decreasing, has range y E (-4, co) and passes through the point P(0, -3). Determine the equation of the new function. Enter m" as m^n. y =Suppose lg (a) =10g2[I) where a: is a positive real number. Express I in terms of :1. Enter m.\" as m'n. I: @@ Find the largest possible interval of a such that the following inequality is satisfied: log, (2x + 1) - log, (1 - 3x) > 1 Enter oo and -oo as infinity and -infinity. Use interval notation. For example, r E (-1, infinity)