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Daniel J Smith Custom TMUA alpha · Q9

Powers & logarithmsAlgebra

For real parameter tt, consider the equation

log⁡3x+log⁡x3=t\log_3 x+\log_x 3=t

with x>0x>0 and x≠1x\neq1. The number of positive solutions xx is

Atwo if ∣t∣>2|t|>2, one if ∣t∣=2|t|=2, and zero if ∣t∣<2|t|<2
Bone if t>0t>0, and zero if t<0t<0
Czero if t>2t>2, one if t=2t=2, and two if 0<t<20<t<2
Done for all real tt
Etwo if t<−2t<-2, zero if t>−2t>-2, and one if t=−2t=-2

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