##log(5*8) = 2log(2)+1 ~~ 1.60206## If ##x y > 0## then: ##log(xy) = log(x)+log(y)## (This follows from ##10^(a+b) = 10^a * 10^b## and the definition of […]
The cube roots of ##8## are ##2## ##2omega## and ##2omega^2## where ##omega=-1/2+sqrt(3)/2 i## is the primitive Complex cube root of ##1##. Here are the cube roots […]
##log(1/100)=-2## First lets assume that the base of the logarithm is 10 sometimes written ##log_(10)##. Next we’ll simplify by using the knowledge that ##log(x^a)=a*log(x)## We can […]
##(16)## First get the equation of the parabola into vertex form: ##y=a(x-h)^2+k## To do this multiply the entire equation by ##1/8##. ##1/8((x-1)^2+32)=1/8(8y)## This simplifies to ##y=1/8(x-1)^2+4## […]
##log x +4log y -3log z## ##log_10x=logx## since base 10 is assumed. ##log((xy^4)/z^3)## ##log(a/b)=loga-logb## ##log xy^4-logz^3## ##logab=loga+logb## ##logx+logy^4-logz^3## ##loga^b=bloga## ##logx+4logy-3logz##