Question 771697
I hope someone can clarify this. I'M CONFUSED!!! 
2(log4 x + logx 4)=5 
My working:
2(log4 x + logx 4)=5
(log4 x + logx 4)=5/2
log4 x + (1/log4 x)=5/2 
Here is where my confusion is. I have 2 different workings.
#1.
log4 x + (1/log4 x)=5/2
Let log4 x = m
Thus, 
m + 1/m = 5/2
[[(m^2)+1]/m]=5/2
(2m^2)+2=5m
(m-2)(2m-1)=0
m=2 or 1/2 
when m=2,
log4 x = m
log4 x = 2
x = 64 
when m=1/2,
log4 x = m
x=2
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#2.
log4 x + (1/log4 x)=5/2
[(log4 x)^2 + (1)/log4 x]=5/2  **** You squared the 1st term for no reason.
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[2(log4 x) + (1)/log4 x]=5/2
Let log4 x = m
Thus, (2m + 1)/m=5/2
4m + 2 =5m
m= 2 
when m=2,
log4 x = m
log4 x = 2
x = 64 
I rechecked again, the correct answer should be m=1/2 and thus x=2.