Solve this function?

Question

(log(z))^2 = log(z^2)

Answer 1

Is this your homework? Just in case it is, I will only post part of the answer and let you figure the rest out.


(log Z )^2 = log Z^2
(log Z)(log Z)= 2log Z divide log Z on both sides
log Z= 2

now remember what base you have with a common log. Keep in mind that Z aill become an exponent if you do this right.

Answer 2

z must be>0 call log x= t
t^2=2t so t(t-2) = 0
t= 0 log z= 0 so z= 1 in any base
t-2=0 t=2 logz=2 and z= (base)^2

Answer 3

log[z] = sqr{2log[z]} = sqr[2]sqr(log[z])
log[z]/sqr(log[z]) = sqr[2] = 2^(1/2)
(log[z])^(1/2) = 2^(1/2)
log[z] = 2
If the log is to base, say let it be b, then raising both sides to b:
b^(log[z]) = b^2
z = b^2