Question

26.si log x = 3 Y log y = 5, calcula:a)log(xy)b)log x²/yc)logx exponente log y d)log ³√xy²e)log y/⁴√xf)logy exonente log(xy)

Answer 1

 logx=3  logy=5

a)  logxy=logx+logy=3+5=8


b)  log x^2/y=log x^2-log y=2logx-logy=2*3-5=6-5=1


c)  logx^logy=logy*logx=5*3=15


d)  lograiz3dexy^2=log(xy^2)^1/3=1/3logxy^2=1/3(logx+logy^2)=
     1/3(logx+2logy)=1/3(3+2*5)=1/3*13=13/3


e)logy/raiz4dex=logy/x^1/4=logy-logx^1/4=logy-1/4logx=5-1/4*3=
    =(5*4-3)/4=17/4



f) logy^log(xy)=log(xy)*logy=(logx+logy)*logy=(3+5)*5=8*5=40