Prove that aloga(x)=xa^{\log_a(x)} = xaloga(x)=x for any valid base a>0,a≠1a > 0, a \neq 1a>0,a=1 and x>0x > 0x>0.
False; this is never true
True; this follows from the definition of logarithm
True only when a=ea = ea=e
True only when x=1x = 1x=1