\log_971\text{ or }\log_861

ajedrezlaproa6j

ajedrezlaproa6j

Answered question

2022-01-20

log971  or  log861

Answer & Explanation

Beverly Smith

Beverly Smith

Beginner2022-01-20Added 42 answers

Ok, so we have that
6164>7181log8(6164)>log9(7181)log8(9)>log9(7181)
By application of the change of base formula and the fact that log8(9)>1, which is trivial.
Deufemiak7

Deufemiak7

Beginner2022-01-21Added 34 answers

log861=log8(64(1364))=2+log8(1364)
log971==2+log9(11081)
Lets
RizerMix

RizerMix

Expert2022-01-27Added 656 answers

Notice that log8:(0,)R is strictly concave. This means that we have log8(x+y2)>log8x+log8y2log8(x+y2)2>log8(xy) Since log89>1, we can conclude that log8(x+y2)2>log8(xy)log89 Let x=61i10 and y=61+i10. Plugging these in (this is okay because imaginary parts disappear), we find that log861>log871log89=log971

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