极限ln(1+2x)/(2^x-1)的(X接近0)

Question

极限ln(1+2x)/(2^x-1)的(X接近0)

Answer 1

当x → 0时,根据等价无穷小替换原则,ln(1 + x) → x ; 2^x - 1 = exp(xln2) - 1 → xln2
极限ln(1+2x)/(2^x-1) = x / xln2 = 1 / ln2