If $x^2$ + $y^2$ = $11xy$, prove that $log(x - y) = frac12log x$ + $frac12log y$ + $log 3$. . Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)use the fact that $tan 2x=sin2x /cos2x$ to prove that $tan 2x=2tan x/(1-tan^2x)$Let $|z|=1, $ prove that $|z^2-3z+1|leq 5$ …need help to prove euler's problem on prime numbers in gelfand algebra text.Simplifying $fraclog(x)x=y$.Prove that from the equalities, $fracx(y+z-x)log x=fracy(x+z-y)log y=fracz(y+x-z)log z$ follows $x^yy^x=y^zz^y=z^xx^z$.Let $z in C^*$ such that $|z^3+frac1z^3|leq 2$ Prove that $|z+frac1z|leq 2$Prove $|x|=maxx,-x$Prove for $ |x|<frac12, x-x^2le log(x+1)le x$.How to solve inequalities with both $log$ and $e$Simplify $frac56logleft(frac54right) - frac16log(2)$ to $logleft(frac54right) - frac16logleft(frac52right)$
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If $x^2$ + $y^2$ = $11xy$, prove that $log(x - y) = frac12log x$ + $frac12log y$ + $log 3$. .
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)use the fact that $tan 2x=sin2x /cos2x$ to prove that $tan 2x=2tan x/(1-tan^2x)$Let $|z|=1, $ prove that $|z^2-3z+1|leq 5$ …need help to prove euler's problem on prime numbers in gelfand algebra text.Simplifying $fraclog(x)x=y$.Prove that from the equalities, $fracx(y+z-x)log x=fracy(x+z-y)log y=fracz(y+x-z)log z$ follows $x^yy^x=y^zz^y=z^xx^z$.Let $z in C^*$ such that $|z^3+frac1z^3|leq 2$ Prove that $|z+frac1z|leq 2$Prove $|x|=maxx,-x$Prove for $ |x|<frac12, x-x^2le log(x+1)le x$.How to solve inequalities with both $log$ and $e$Simplify $frac56logleft(frac54right) - frac16log(2)$ to $logleft(frac54right) - frac16logleft(frac52right)$
$begingroup$
If $x^2$ + $y^2$ = $11xy$, prove that $log(x - y) = frac12log x$ + $frac12log y$ + $log 3$.
I don't even know where to begin, this is the first time I have encountered a problem like this, please guide me through this proof. Thanks.
algebra-precalculus
asked Mar 31 at 18:44
AntonioAntonio
296
$endgroup$
add a comment |
$begingroup$
If $x^2$ + $y^2$ = $11xy$, prove that $log(x - y) = frac12log x$ + $frac12log y$ + $log 3$.
I don't even know where to begin, this is the first time I have encountered a problem like this, please guide me through this proof. Thanks.
algebra-precalculus
asked Mar 31 at 18:44
AntonioAntonio
296
$endgroup$
7
$begingroup$
Hint: subtract $2xy$ from both sides
$endgroup$
– Wojowu
Mar 31 at 18:45
$begingroup$
Thank you, I feel so dumb right now, I hope I can improve my intuition.
$endgroup$
– Antonio
Mar 31 at 18:55
$begingroup$
$lg$ is not a common usage, prefer $ln$ or $log$ or $log_2$, at least the notation needs to be explicited.
$endgroup$
– zwim
Mar 31 at 19:48
add a comment |
$begingroup$
If $x^2$ + $y^2$ = $11xy$, prove that $log(x - y) = frac12log x$ + $frac12log y$ + $log 3$.
I don't even know where to begin, this is the first time I have encountered a problem like this, please guide me through this proof. Thanks.
algebra-precalculus
asked Mar 31 at 18:44
AntonioAntonio
296
$endgroup$
If $x^2$ + $y^2$ = $11xy$, prove that $log(x - y) = frac12log x$ + $frac12log y$ + $log 3$.
I don't even know where to begin, this is the first time I have encountered a problem like this, please guide me through this proof. Thanks.
algebra-precalculus
algebra-precalculus
asked Mar 31 at 18:44
AntonioAntonio
296
asked Mar 31 at 18:44
AntonioAntonio
296
edited Mar 31 at 21:16
Antonio
asked Mar 31 at 18:44
AntonioAntonio
296
asked Mar 31 at 18:44
AntonioAntonio
296
asked Mar 31 at 18:44
AntonioAntonio
296
296
7
$begingroup$
Hint: subtract $2xy$ from both sides
$endgroup$
– Wojowu
Mar 31 at 18:45
$begingroup$
Thank you, I feel so dumb right now, I hope I can improve my intuition.
$endgroup$
– Antonio
Mar 31 at 18:55
$begingroup$
$lg$ is not a common usage, prefer $ln$ or $log$ or $log_2$, at least the notation needs to be explicited.
$endgroup$
– zwim
Mar 31 at 19:48
add a comment |
7
$begingroup$
Hint: subtract $2xy$ from both sides
$endgroup$
– Wojowu
Mar 31 at 18:45
$begingroup$
Thank you, I feel so dumb right now, I hope I can improve my intuition.
$endgroup$
– Antonio
Mar 31 at 18:55
$begingroup$
$lg$ is not a common usage, prefer $ln$ or $log$ or $log_2$, at least the notation needs to be explicited.
$endgroup$
– zwim
Mar 31 at 19:48
7
7
$begingroup$
Hint: subtract $2xy$ from both sides
$endgroup$
– Wojowu
Mar 31 at 18:45
$begingroup$
Hint: subtract $2xy$ from both sides
$endgroup$
– Wojowu
Mar 31 at 18:45
$begingroup$
Thank you, I feel so dumb right now, I hope I can improve my intuition.
$endgroup$
– Antonio
Mar 31 at 18:55
$begingroup$
Thank you, I feel so dumb right now, I hope I can improve my intuition.
$endgroup$
– Antonio
Mar 31 at 18:55
$begingroup$
$lg$ is not a common usage, prefer $ln$ or $log$ or $log_2$, at least the notation needs to be explicited.
$endgroup$
– zwim
Mar 31 at 19:48
$begingroup$
$lg$ is not a common usage, prefer $ln$ or $log$ or $log_2$, at least the notation needs to be explicited.
$endgroup$
– zwim
Mar 31 at 19:48
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
$x^2+y^2=11xy$ can be written as $x^2+y^2-2xy=9xyLongrightarrow(x-y)^2=9xy$ or $x-y=3sqrt xsqrt y$. Apply log on both sides, you get your result.
answered Mar 31 at 18:53
ProblemBookProblemBook
796
$endgroup$
$begingroup$
Thank you, I feel so dumb right now, I hope I can improve my intuition. The problem was so simple yet I got scared and lost all hope and gave up easily.
$endgroup$
– Antonio
Mar 31 at 18:55
add a comment |
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1 Answer
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1 Answer
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$begingroup$
$x^2+y^2=11xy$ can be written as $x^2+y^2-2xy=9xyLongrightarrow(x-y)^2=9xy$ or $x-y=3sqrt xsqrt y$. Apply log on both sides, you get your result.
answered Mar 31 at 18:53
ProblemBookProblemBook
796
$endgroup$
$begingroup$
Thank you, I feel so dumb right now, I hope I can improve my intuition. The problem was so simple yet I got scared and lost all hope and gave up easily.
$endgroup$
– Antonio
Mar 31 at 18:55
add a comment |
$begingroup$
$x^2+y^2=11xy$ can be written as $x^2+y^2-2xy=9xyLongrightarrow(x-y)^2=9xy$ or $x-y=3sqrt xsqrt y$. Apply log on both sides, you get your result.
answered Mar 31 at 18:53
ProblemBookProblemBook
796
$endgroup$
$begingroup$
Thank you, I feel so dumb right now, I hope I can improve my intuition. The problem was so simple yet I got scared and lost all hope and gave up easily.
$endgroup$
– Antonio
Mar 31 at 18:55
add a comment |
$begingroup$
$x^2+y^2=11xy$ can be written as $x^2+y^2-2xy=9xyLongrightarrow(x-y)^2=9xy$ or $x-y=3sqrt xsqrt y$. Apply log on both sides, you get your result.
answered Mar 31 at 18:53
ProblemBookProblemBook
796
$endgroup$
$x^2+y^2=11xy$ can be written as $x^2+y^2-2xy=9xyLongrightarrow(x-y)^2=9xy$ or $x-y=3sqrt xsqrt y$. Apply log on both sides, you get your result.
answered Mar 31 at 18:53
ProblemBookProblemBook
796
answered Mar 31 at 18:53
ProblemBookProblemBook
796
answered Mar 31 at 18:53
ProblemBookProblemBook
796
answered Mar 31 at 18:53
ProblemBookProblemBook
796
796
$begingroup$
Thank you, I feel so dumb right now, I hope I can improve my intuition. The problem was so simple yet I got scared and lost all hope and gave up easily.
$endgroup$
– Antonio
Mar 31 at 18:55
add a comment |
$begingroup$
Thank you, I feel so dumb right now, I hope I can improve my intuition. The problem was so simple yet I got scared and lost all hope and gave up easily.
$endgroup$
– Antonio
Mar 31 at 18:55
$begingroup$
Thank you, I feel so dumb right now, I hope I can improve my intuition. The problem was so simple yet I got scared and lost all hope and gave up easily.
$endgroup$
– Antonio
Mar 31 at 18:55
$begingroup$
Thank you, I feel so dumb right now, I hope I can improve my intuition. The problem was so simple yet I got scared and lost all hope and gave up easily.
$endgroup$
– Antonio
Mar 31 at 18:55
add a comment |
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7
$begingroup$
Hint: subtract $2xy$ from both sides
$endgroup$
– Wojowu
Mar 31 at 18:45
$begingroup$
Thank you, I feel so dumb right now, I hope I can improve my intuition.
$endgroup$
– Antonio
Mar 31 at 18:55
$begingroup$
$lg$ is not a common usage, prefer $ln$ or $log$ or $log_2$, at least the notation needs to be explicited.
$endgroup$
– zwim
Mar 31 at 19:48