Question

Oblicz x, gry:
a) x=log₅9+2*(log₅1-log₅3),
b) x=log₃2²+log₃4,5²-2*log₅ √5 ,
c) log₂x=3

Zadanie ze szkoły średniej ; )

Answer 1

A) x=log₅9+2*(log₅1-log₅3)=2+2*log3 1/3=2+2*(-1)=2-2=0
b) x=log₃2²+log₃4,5²-2*log₅ √5 =2log₃2+2log₃4,5-2log₃√5 =2(log₃(2*4,5/√5 )=
2*log₃9-2log₃/5=2*2-2log₃/5=4-2log₃/5
c) log₂x=3
x=2^3
x=8

Answer 2

A) x=log₅9+2*(log₅1-log₅3),
x=log₅9+2*(log₅⅓)
x=log₅9+log₅(⅓)²
x=log₅9*(⅓)²
x=log₅9*1/9
x=log₅1
x=0

b) x=log₃2²+log₃4,5²-2*log₅ √5
x=log₃4+log₃20,25-log₅5
x=log₃4*20,25-1
x=log₃81-1
x=log₃3⁴-1
x=4log₃3-1
x=4-1
x=3

c) log₂x=3
x=2³
x=8