Evaluate the limit if exists, `lim_(x->1)[{ln(1+x)-ln2}{3.4^[x-1]-3x}]/[{(7+x)^[1/3]-(1+3x)^[1/2]}sin(x-1)]`

Evaluate the limit if exists,lim_(x rarr1)({ln(1+x)-ln2}{3.4^(x-1)-3x})/({(7+x)^((1)/(3))-(1+3x)^((1)/(2))}sin(x-1))

Evaluate the limits, if exist (lim)_(xrarr0)(log(1+x^3))/(sin^3x)

Evaluate the limits,if exist (lim)_(x rarr0)(log(1+x^(3)))/(sin^(3)x)

Evaluate the limit: (lim)_(xvec 1)(sin(log x))/(log x)

Evaluate the limits lim_(x to 0) (1+x)^(1//3x)

Evaluate the following limits, if they exist : lim_(x to 3)[x(x+1)]

Evaluate the following limit if they exist : lim_(x rarr -1) (x^3-3x+1)/(x-1) .

Evaluate the following limit: (lim)_(x->0)("log"(1+x))/(3^x-1)

Evaluate the following limits, if they exist : lim_(x to 1)(x^(3)-x^(2)+1)

Evaluate the following limit : lim_(x rarr 0)(log(1+3x))/(3^x-1) .