Use formula `lim_(x->0)(a^x-1)/x=log(a)` to find `lim_(x->0)(2^x-1)/((1+x)^(1/2)-1)`

Use the formula lim_(x to 0 ) (a^(x) - 1) / x log_(e) a , to find lim_( x to 0) (2^(x)-1)/((1+x)^(1//2) - 1) .

Evaluate: lim_(x rarr0)(2^(x)-1)/((1+x)^((1)/(2))-1)

lim_(x to 0) (2^(x) - 1)/(sqrt(1 + x) - 1) =

Evaluate : lim_(x rarr0)(a^(2x)-1)/(x)

lim_(x rarr0)(log(1+x))/(x)=1

(7) Find the value of lim_(x->0) ((e^(x)-1) log(1+x))/(x^(2))

lim_(x rarr0)((e^(x)-1)log(1+x))/(sin x)

Find the value of lim_(x->0) log(1+x)/(4^(x)-1)=

lim_(x rarr0)(x cos x-log(1+x))/(x^(2))