решите уравнение log2(x)+logx(2)=2,5

Question

решите уравнение log2(x)+logx(2)=2,5

Answer 1

LogA B=1/logB A
log2(x)+logx(2)=2.5
log2(x)+1/log2(x)=5/2
log2(x=t
2t2-5t+2=0
t12=(5+-корень(25-16))/4=(5+-3)/4= 2 1/2
log2 x=2
x=4
log2 x=1/2
x=корень(2)