FInd the limit x approaches 0

Question

If x and y are both positive, evaluate

lim p appraoches 0 ( (ln(0.3x^p+0.7y^p))/p

and lim p appraches 0 (0.3x^p + 0.7y^p)^1/p

Answer 1

attempt 1 ... let x=y to form a straight line path ... thus lim ln(.3x^p+.7y^p)/p = lim ln(x^p)/p= lim pln(x)/p= lnx

attempt 1 ... let x=y to form a straight line path ... thus lim (.3x^p+.7y^p)^1/p= lim(x^p)^1/p= x