Question

Obliczyć
9^(log(3)4+log(1/3)2)=?

log(x)4>2

Answer 1

Obliczyć
9^(log(3)4+log(1/3)2)=?

9^(log(3)4+log(1/3)2)=9^log(3)4 *9^log(1/3)2=3^2log(3)4 *3^2log(1/3)2=

3^log(3)16 *3^log(1/3)4=3^(log(3)16 +log(1/3)4)=
3^(log(3)16 +log(3)4/log(3) 1/3)=3^(log(3)16 +log(3)4/-1)=
3^(log(3)16 -log(3)4)=3^(log(3)16:4)=3^(log(3)4)=4

log(x)4>2
4>x² /√ gdy x>1
2>IxI
x∈(-2;2) i x>1
czyli:
x∈(1;2)

4<x² /√ gdy 0<x<1
2<IxI
x∈(-∞;-2)u(2;+∞) i 0<x<1
czyli:
x∈Ф
odp.x∈(1;2)