Come risolvi # (ln x) ^ 2 = ln x ^ 2 #?
Risposta:
#x=1color(white)("XXX")orcolor(white)("XXX")x=e^2#
Spiegazione:
Ricorda: #ln(x^2)=2ln(x)#
lasciare #k=ln(x)#
Quindi
#color(white)("XXX")(ln(x))^2=ln(x^2)#
รจ equivalente
#color(white)("XXX")k^2=2k#
#color(white)("XXX")k^2-2k=0#
#color(white)("XXX")k(k-2)=0#
#color(white)("XXX"){:
(k=0,color(white)("XX")orcolor(white)("XX"),k=2),
(rarr ln(x)=0,,rarr ln(x)=2),
(rarr e^0=x,,rarr e^2=x),
(rarr x=1,,rarr x=e^2)
:}#