Find x with $4^{x-1} = 9cdot x^{3-x}+7$
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1
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How to solve this exponential functuion?
$4^{x-1} = 9cdot x^{3-x}+7$
The solution is $x=3$.
exponential-function
edited Nov 12 at 17:15
Richard
3521110
asked Nov 12 at 16:56
ScoobyDuh
405
add a comment |
up vote
1
down vote
favorite
How to solve this exponential functuion?
$4^{x-1} = 9cdot x^{3-x}+7$
The solution is $x=3$.
exponential-function
edited Nov 12 at 17:15
Richard
3521110
asked Nov 12 at 16:56
ScoobyDuh
405
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
How to solve this exponential functuion?
$4^{x-1} = 9cdot x^{3-x}+7$
The solution is $x=3$.
exponential-function
edited Nov 12 at 17:15
Richard
3521110
asked Nov 12 at 16:56
ScoobyDuh
405
How to solve this exponential functuion?
$4^{x-1} = 9cdot x^{3-x}+7$
The solution is $x=3$.
exponential-function
exponential-function
edited Nov 12 at 17:15
Richard
3521110
asked Nov 12 at 16:56
ScoobyDuh
405
edited Nov 12 at 17:15
Richard
3521110
asked Nov 12 at 16:56
ScoobyDuh
405
edited Nov 12 at 17:15
Richard
3521110
edited Nov 12 at 17:15
Richard
3521110
edited Nov 12 at 17:15
Richard
3521110
3521110
asked Nov 12 at 16:56
ScoobyDuh
405
asked Nov 12 at 16:56
ScoobyDuh
405
asked Nov 12 at 16:56
ScoobyDuh
405
405
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
up vote
3
down vote
accepted
Equations such as this very rarely have closed-form solutions, and there is no general method for finding them. In this case it's easy to verify that $x=3$ works. Using the fact that for $x > 2$, the right side is decreasing while the left side is increasing, it's not hard to show this is the only positive real solution.
answered Nov 12 at 17:32
Robert Israel
313k23206452
So this is the only way to find the solution?
– ScoobyDuh
Nov 12 at 18:56
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
Equations such as this very rarely have closed-form solutions, and there is no general method for finding them. In this case it's easy to verify that $x=3$ works. Using the fact that for $x > 2$, the right side is decreasing while the left side is increasing, it's not hard to show this is the only positive real solution.
answered Nov 12 at 17:32
Robert Israel
313k23206452
So this is the only way to find the solution?
– ScoobyDuh
Nov 12 at 18:56
add a comment |
up vote
3
down vote
accepted
Equations such as this very rarely have closed-form solutions, and there is no general method for finding them. In this case it's easy to verify that $x=3$ works. Using the fact that for $x > 2$, the right side is decreasing while the left side is increasing, it's not hard to show this is the only positive real solution.
answered Nov 12 at 17:32
Robert Israel
313k23206452
So this is the only way to find the solution?
– ScoobyDuh
Nov 12 at 18:56
add a comment |
up vote
3
down vote
accepted
up vote
3
down vote
accepted
Equations such as this very rarely have closed-form solutions, and there is no general method for finding them. In this case it's easy to verify that $x=3$ works. Using the fact that for $x > 2$, the right side is decreasing while the left side is increasing, it's not hard to show this is the only positive real solution.
answered Nov 12 at 17:32
Robert Israel
313k23206452
Equations such as this very rarely have closed-form solutions, and there is no general method for finding them. In this case it's easy to verify that $x=3$ works. Using the fact that for $x > 2$, the right side is decreasing while the left side is increasing, it's not hard to show this is the only positive real solution.
answered Nov 12 at 17:32
Robert Israel
313k23206452
answered Nov 12 at 17:32
Robert Israel
313k23206452
answered Nov 12 at 17:32
Robert Israel
313k23206452
answered Nov 12 at 17:32
Robert Israel
313k23206452
313k23206452
So this is the only way to find the solution?
– ScoobyDuh
Nov 12 at 18:56
add a comment |
So this is the only way to find the solution?
– ScoobyDuh
Nov 12 at 18:56
So this is the only way to find the solution?
– ScoobyDuh
Nov 12 at 18:56
So this is the only way to find the solution?
– ScoobyDuh
Nov 12 at 18:56
add a comment |
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