Question

Log 3 32 • log2 25 • log 0.2 3

Answer 1

Log₃32*log₂25*log₀,₂3=-10
переход к новому основанию 2.
1.  log₃32=log₃2⁵=5*log₃2=5*(log₂2/log₂3)=5*(1/log₂3)=5/log₂3
2.  log₂25=log₂5²=2*log₂5
3.  log₀,₂3=log₁/₅5=log₂3/log₂(1/5)=log₂3/(log₂5⁻¹)=-log₂3/log₂5
4.  (5/log₂3)*(2*log₂5)*(-log₂3/log₂5)=5*2*(-1)=-10