16=2^4
logx^2(16)=logx^2(2^4)=4 logx^2(2)=4/log2(x^2)=4/(2 log2(x))=2/log2(x)
log2x(64)=6 log2x(2)=6/log2(2x)=6/(log2(2)+log2(x))=6/(1+log2(x))
Notam log2(x)=y
2/y + 6/(1+y) = 3
2(1+y)+6y=3y(1+y)
2 + 8y = 3y + 3y^2
3y^2 - 5y - 2 = 0
3y^2 - 3y - 2y - 2 =0
Discriminantul: 5^2 + 4 * 3 * 2= 25 + 24= 49 = 7^2
y1=(5+7)/6 = 12/6 = 2
y2=(5-7)/6 = -1/3
log2(x) = 2, deci x=4
log2(x) = -1/3, deci x=2^(-1/3)=-1/rad_ordin_3_din(2)
Verificare:
logx^2(16)+log2x(64) = log16(16) + log8(8^2) = 1 + 2 = 3 (verifica)
La ailalta, nu mai am rabdare....
