Cho a > 0, a khác 1, a^1/2=b Tính: a) loga b; b) loga (a^3b^2);
Cho a > 0, a ≠ 1, a12=b. Tính:
a) loga b;
a) loga b;
b) loga (a3b2);
c) log√a(ab);
d) logab(a√b).
Với a > 0, a ≠ 1 và a12=b nên b > 0. Ta có:
a) logab=logaa12=12.
b) loga(a3b2)=loga[a3.(a12)2]=loga(a3.a)=logaa4=4.
c) log√a(ab)=loga12(aa12)=2logaa1−12=2logaa12=2⋅12=a.
d) logab(a√b)=loga⋅a12(a√a12)=loga32(a.a14)=23loga(a1+14)=23logaa54=23.54=56.
a) logab=logaa12=12.
b) loga(a3b2)=loga[a3.(a12)2]=loga(a3.a)=logaa4=4.
c) log√a(ab)=loga12(aa12)=2logaa1−12=2logaa12=2⋅12=a.
d) logab(a√b)=loga⋅a12(a√a12)=loga32(a.a14)=23loga(a1+14)=23logaa54=23.54=56.