Question

prove that log ABC is equalent log A + log b + log c

Answer 1

Log(XY) = logX+LogY

therefore,
Log A+log B = log AB
LogA + log B + logC = log ABC

Answer 2

$let \: log a = x \\ a = c^{x} \\ logb = y \\ b = {c}^{y} \\ consider \\ a b = {c}^{x} {c}^{y} \\ ab = {c}^{x + y} \\ logab = x + y \\ from \: the \: above \\ logab = loga + logb \\ since \: c \: is \: base \: of \: logarithm$
similarly we can expand to
logABC= logAB+logC=logA+logB+logC