Question

X do potęgi log przy podstawie 2 z X = 64X
log2X
X = 64X

Answer 1

X ^ log ₂ X = 64X /log
D=x∈R+

log[X ^ log ₂ X]=log(64X)
log ₂ X*logX =log64+logX
log ₂ X*log₂X/log₂10 =log64+log₂X/log₂10
log₂²X/log₂10 =log64+log₂X/log₂10

log₂X=t

t²/log₂10=log64+t/log₂10
t²/log₂10 - t/log₂10 -log64=0

Δ=1/log₂²10+ 4* log64/log₂10=1/log₂²10+ 4* log₂64/log₂10*log₂10=
=1/log₂²10+ 4* log₂2⁶/log₂²10=1/log₂²10+ 4*6/log₂²10=
25/log₂²10

√Δ=5/log₂10

t₁=(1/log₂10-5/log₂10)/ [2/log₂10]=-4/log₂10*log₂10/2=-4/2=-2
t₂=(1/log₂10+5/log₂10)/ [2/log₂10]=6/log₂10*log₂10/2=6/2=3

log₂X=-2 lub log₂X=3
x=2⁻² lub x=2³
x=1/4 lub x=8