Помогите с логарифмами 1) log3log5 125 2) lg16/lg2 3) 2log5 27 - log5 81 - 2log5 15

Question

Помогите с логарифмами
1) log3log5 125
2) lg16/lg2
3) 2log5 27 - log5 81 - 2log5 15

Answer 1

Log₃log₅125=log₃log₅5³=log₃(3*log₅5)=log₃3=1.
lg16/lg2=lg(2⁴)/lg2=4*lg2/lg2=4.
2*log₅27-log₅81-2*log₅15=2*log₅3³-log₅3⁴-2*log₅15=
=log₅3⁶-log3⁴-log₅15²=log₅3⁶/(3⁴*15²)=log(9/225)=log(1/25)=log₅5⁻²=-2.

Answer 2

1)log3(log5 125)=log3(3)=1