lim(x->∞) [ln(2^x+3^x)^(1/x)]=lim(x->∞)[ ln(2^x+3^x) ]/x ( ∞/∞)=lim(x->∞) [(ln2).2^x+ (ln3).3^x] /(2^x+3^x)=lim(x->∞) [ (ln2).(2/3)^x+ (ln3) ] /[(2/3)^x+1]= ln3