Question

极限x趋向负无穷大.㏑(1加3的x方)除以㏑( 1加2x方)

极限x趋向负无穷大.㏑(1加3的x方)除以㏑( 1加2x方)

Answer 1

lim(x→-∞)ln(1+3^x)/ln(1+2^x)
=lim(x→-∞)[ln3/(1+3^x)]/[ln2/(1+2^x)]
=(ln3/ln2)lim(x→-∞)(1+2^x)/(1+3^x)
=(ln3/ln2)(1+0)/(1+0)
=ln3/ln2

Answer 2

lim(x-->-oo)ln(1+3^x)/ln(1+2^x)
=lim(x-->+oo)ln(1+1/3^x)/ln(1+1/2^x)
=lim(x-->+oo)(1/3^x)/(1/2^x)
=lim(x-->+oo)(2/3)^x
=0