Solve this : $ x^frac 34 log_2^2 x + log_2 (x-5/4) = sqrt 2 $
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The question : $$ x^frac 34 log_2^2 x + log_2 left(x-frac 54right) = sqrt 2 $$
My try at it : I think that the whole equation should be converted to log with base 2. What to do next?
logarithms
asked Apr 14 '17 at 14:33
Esha Mukhopadhyay
35
 |Â
show 9 more comments
up vote
0
down vote
favorite
The question : $$ x^frac 34 log_2^2 x + log_2 left(x-frac 54right) = sqrt 2 $$
My try at it : I think that the whole equation should be converted to log with base 2. What to do next?
logarithms
asked Apr 14 '17 at 14:33
Esha Mukhopadhyay
35
Does $log^2 x$ mean $log(log x)$ or $(log x)^2$
– DHMO
Apr 14 '17 at 14:39
1
The title and the question have different equations in them. Which one do you mean?
– AsafHaas
Apr 14 '17 at 14:40
$ (log_2 x) ^ 2 $
– Esha Mukhopadhyay
Apr 14 '17 at 14:41
@AsafHaas its the same. i hav copied it from the title.
– Esha Mukhopadhyay
Apr 14 '17 at 14:41
By executing your idea and let $y=log_2 x$, we get $1/2=y(3y^2/4+log_2(x-5/4))$
– didgogns
Apr 14 '17 at 14:43
 |Â
show 9 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
The question : $$ x^frac 34 log_2^2 x + log_2 left(x-frac 54right) = sqrt 2 $$
My try at it : I think that the whole equation should be converted to log with base 2. What to do next?
logarithms
asked Apr 14 '17 at 14:33
Esha Mukhopadhyay
35
The question : $$ x^frac 34 log_2^2 x + log_2 left(x-frac 54right) = sqrt 2 $$
My try at it : I think that the whole equation should be converted to log with base 2. What to do next?
logarithms
logarithms
asked Apr 14 '17 at 14:33
Esha Mukhopadhyay
35
asked Apr 14 '17 at 14:33
Esha Mukhopadhyay
35
edited Apr 14 '17 at 15:09
asked Apr 14 '17 at 14:33
Esha Mukhopadhyay
35
asked Apr 14 '17 at 14:33
Esha Mukhopadhyay
35
asked Apr 14 '17 at 14:33
Esha Mukhopadhyay
35
35
Does $log^2 x$ mean $log(log x)$ or $(log x)^2$
– DHMO
Apr 14 '17 at 14:39
1
The title and the question have different equations in them. Which one do you mean?
– AsafHaas
Apr 14 '17 at 14:40
$ (log_2 x) ^ 2 $
– Esha Mukhopadhyay
Apr 14 '17 at 14:41
@AsafHaas its the same. i hav copied it from the title.
– Esha Mukhopadhyay
Apr 14 '17 at 14:41
By executing your idea and let $y=log_2 x$, we get $1/2=y(3y^2/4+log_2(x-5/4))$
– didgogns
Apr 14 '17 at 14:43
 |Â
show 9 more comments
Does $log^2 x$ mean $log(log x)$ or $(log x)^2$
– DHMO
Apr 14 '17 at 14:39
1
The title and the question have different equations in them. Which one do you mean?
– AsafHaas
Apr 14 '17 at 14:40
$ (log_2 x) ^ 2 $
– Esha Mukhopadhyay
Apr 14 '17 at 14:41
@AsafHaas its the same. i hav copied it from the title.
– Esha Mukhopadhyay
Apr 14 '17 at 14:41
By executing your idea and let $y=log_2 x$, we get $1/2=y(3y^2/4+log_2(x-5/4))$
– didgogns
Apr 14 '17 at 14:43
Does $log^2 x$ mean $log(log x)$ or $(log x)^2$
– DHMO
Apr 14 '17 at 14:39
Does $log^2 x$ mean $log(log x)$ or $(log x)^2$
– DHMO
Apr 14 '17 at 14:39
1
1
The title and the question have different equations in them. Which one do you mean?
– AsafHaas
Apr 14 '17 at 14:40
The title and the question have different equations in them. Which one do you mean?
– AsafHaas
Apr 14 '17 at 14:40
$ (log_2 x) ^ 2 $
– Esha Mukhopadhyay
Apr 14 '17 at 14:41
$ (log_2 x) ^ 2 $
– Esha Mukhopadhyay
Apr 14 '17 at 14:41
@AsafHaas its the same. i hav copied it from the title.
– Esha Mukhopadhyay
Apr 14 '17 at 14:41
@AsafHaas its the same. i hav copied it from the title.
– Esha Mukhopadhyay
Apr 14 '17 at 14:41
By executing your idea and let $y=log_2 x$, we get $1/2=y(3y^2/4+log_2(x-5/4))$
– didgogns
Apr 14 '17 at 14:43
By executing your idea and let $y=log_2 x$, we get $1/2=y(3y^2/4+log_2(x-5/4))$
– didgogns
Apr 14 '17 at 14:43
 |Â
show 9 more comments
1 Answer
1
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oldest
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up vote
0
down vote
taking the logarithm on both sides of your equation we obatin
$$left(frac34left(fracln(x)ln(2)right)^2+fraclnleft(x-frac54right)ln(2)right)ln(x)=frac12ln(2)$$ and here you can take a numerical method
with such a method we obtain $$xapprox 2.050105808$$
answered Apr 14 '17 at 14:45
Dr. Sonnhard Graubner
68.9k32760
this is turning out to be a tricky thing. can u please solve it?
– Esha Mukhopadhyay
Apr 14 '17 at 14:58
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
taking the logarithm on both sides of your equation we obatin
$$left(frac34left(fracln(x)ln(2)right)^2+fraclnleft(x-frac54right)ln(2)right)ln(x)=frac12ln(2)$$ and here you can take a numerical method
with such a method we obtain $$xapprox 2.050105808$$
answered Apr 14 '17 at 14:45
Dr. Sonnhard Graubner
68.9k32760
this is turning out to be a tricky thing. can u please solve it?
– Esha Mukhopadhyay
Apr 14 '17 at 14:58
add a comment |Â
up vote
0
down vote
taking the logarithm on both sides of your equation we obatin
$$left(frac34left(fracln(x)ln(2)right)^2+fraclnleft(x-frac54right)ln(2)right)ln(x)=frac12ln(2)$$ and here you can take a numerical method
with such a method we obtain $$xapprox 2.050105808$$
answered Apr 14 '17 at 14:45
Dr. Sonnhard Graubner
68.9k32760
this is turning out to be a tricky thing. can u please solve it?
– Esha Mukhopadhyay
Apr 14 '17 at 14:58
add a comment |Â
up vote
0
down vote
up vote
0
down vote
taking the logarithm on both sides of your equation we obatin
$$left(frac34left(fracln(x)ln(2)right)^2+fraclnleft(x-frac54right)ln(2)right)ln(x)=frac12ln(2)$$ and here you can take a numerical method
with such a method we obtain $$xapprox 2.050105808$$
answered Apr 14 '17 at 14:45
Dr. Sonnhard Graubner
68.9k32760
taking the logarithm on both sides of your equation we obatin
$$left(frac34left(fracln(x)ln(2)right)^2+fraclnleft(x-frac54right)ln(2)right)ln(x)=frac12ln(2)$$ and here you can take a numerical method
with such a method we obtain $$xapprox 2.050105808$$
answered Apr 14 '17 at 14:45
Dr. Sonnhard Graubner
68.9k32760
edited Apr 14 '17 at 15:24
answered Apr 14 '17 at 14:45
Dr. Sonnhard Graubner
68.9k32760
answered Apr 14 '17 at 14:45
Dr. Sonnhard Graubner
68.9k32760
answered Apr 14 '17 at 14:45
Dr. Sonnhard Graubner
68.9k32760
68.9k32760
this is turning out to be a tricky thing. can u please solve it?
– Esha Mukhopadhyay
Apr 14 '17 at 14:58
add a comment |Â
this is turning out to be a tricky thing. can u please solve it?
– Esha Mukhopadhyay
Apr 14 '17 at 14:58
this is turning out to be a tricky thing. can u please solve it?
– Esha Mukhopadhyay
Apr 14 '17 at 14:58
this is turning out to be a tricky thing. can u please solve it?
– Esha Mukhopadhyay
Apr 14 '17 at 14:58
add a comment |Â
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Does $log^2 x$ mean $log(log x)$ or $(log x)^2$
– DHMO
Apr 14 '17 at 14:39
1
The title and the question have different equations in them. Which one do you mean?
– AsafHaas
Apr 14 '17 at 14:40
$ (log_2 x) ^ 2 $
– Esha Mukhopadhyay
Apr 14 '17 at 14:41
@AsafHaas its the same. i hav copied it from the title.
– Esha Mukhopadhyay
Apr 14 '17 at 14:41
By executing your idea and let $y=log_2 x$, we get $1/2=y(3y^2/4+log_2(x-5/4))$
– didgogns
Apr 14 '17 at 14:43