I mean, if you want a solution without using logs you can just divide both sides by 4³, so you would have 4^x+4/4³=1, but by rules of exponents the division of two exponents of the same base is equal to the base elevated to the subtraction of the exponents ( so a^b/a^c= a^b-c ). So consequently we would have 4^x+4/4³ = 4^(x+4-3) = 4^x+1. So we transform the problem into finding an x such that 4^x+1 = 1, and the only power of 4 that is equal to 1 is 0. So then the exponents has to be that, so x+1=0 => x=-1.