Cho logab = 4. Tính: a) log a (a^1/2 b^5) b) log a (a căn b/ b^3 căn a)

a) logaa12b5=logaa12+logab5
=12.logaa+5.logab=12.1+5.4=412.
b) logaabba3=logaa.b12a13b
=logaaa13.b12b=logaa1−13.b12−1
=logaa23b−12=logaa23+logab−12
=23logaa−12logab=23.1−12.4=−43.
c) loga3b2a2b3=logaa2b3logaa3b2
=logaa2+logab3logaa3+logab2
=2+3logab3+2logab=2+3.43+2.4=1411.
d) logab3ab4=logaab4logaab3
=logaab124logaab13=logaab1214logaab13 =logaa14.b12.14logaab13=logaa14b18logaab13=logaa14+logab18logaa+logab13=14+18logab1+13logab=14+18.41+13.4=928.