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
#2.
log4 x + (1/log4 x)=5/2
[(log4 x)^2 + (1)/log4 x]=5/2
[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. Can anyone tell me where did i do wrong for #2 working? And can anyone guide me how to determine the correct answer for #1 working? Please help me. Your help is much appreciated.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! 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
===========================================================
#2.
log4 x + (1/log4 x)=5/2
[(log4 x)^2 + (1)/log4 x]=5/2 **** You squared the 1st term for no reason.
====================================
[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.
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