solving exponential function with linear function
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0
down vote
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I want to solve the solutions to x for below equation.
For, $a,b,c,dinmathbb{R}$, $x^a(bx+c) = d$.
Is it possible to express the solution of $x$ with $a,b,c,d$ for this equation? If possible, how can I find it?
algebra-precalculus
asked Nov 19 at 5:42
kyub
325
add a comment |
up vote
0
down vote
favorite
I want to solve the solutions to x for below equation.
For, $a,b,c,dinmathbb{R}$, $x^a(bx+c) = d$.
Is it possible to express the solution of $x$ with $a,b,c,d$ for this equation? If possible, how can I find it?
algebra-precalculus
asked Nov 19 at 5:42
kyub
325
1
Even when $a$ is a positive integer you cannot solve it explicitly.
– Kavi Rama Murthy
Nov 19 at 5:44
@KaviRamaMurthy then, is there any way to get an approximated solution of $x$?
– kyub
Nov 19 at 5:52
Only a numerical method would work. This is not an equation that would yield a closed form solution.
– Rebellos
Nov 19 at 6:03
Numerical schemes could be regula falsi or newton's method. However to which solution the scheme converges (and if it converges at all) is highly dependent on the starting values and the explicit values of $a,b,c,d$. Especially the value of $a$ is crucial for the behaviour.
– maxmilgram
Nov 19 at 6:36
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I want to solve the solutions to x for below equation.
For, $a,b,c,dinmathbb{R}$, $x^a(bx+c) = d$.
Is it possible to express the solution of $x$ with $a,b,c,d$ for this equation? If possible, how can I find it?
algebra-precalculus
asked Nov 19 at 5:42
kyub
325
I want to solve the solutions to x for below equation.
For, $a,b,c,dinmathbb{R}$, $x^a(bx+c) = d$.
Is it possible to express the solution of $x$ with $a,b,c,d$ for this equation? If possible, how can I find it?
algebra-precalculus
algebra-precalculus
asked Nov 19 at 5:42
kyub
325
asked Nov 19 at 5:42
kyub
325
asked Nov 19 at 5:42
kyub
325
asked Nov 19 at 5:42
kyub
325
asked Nov 19 at 5:42
kyub
325
325
1
Even when $a$ is a positive integer you cannot solve it explicitly.
– Kavi Rama Murthy
Nov 19 at 5:44
@KaviRamaMurthy then, is there any way to get an approximated solution of $x$?
– kyub
Nov 19 at 5:52
Only a numerical method would work. This is not an equation that would yield a closed form solution.
– Rebellos
Nov 19 at 6:03
Numerical schemes could be regula falsi or newton's method. However to which solution the scheme converges (and if it converges at all) is highly dependent on the starting values and the explicit values of $a,b,c,d$. Especially the value of $a$ is crucial for the behaviour.
– maxmilgram
Nov 19 at 6:36
add a comment |
1
Even when $a$ is a positive integer you cannot solve it explicitly.
– Kavi Rama Murthy
Nov 19 at 5:44
@KaviRamaMurthy then, is there any way to get an approximated solution of $x$?
– kyub
Nov 19 at 5:52
Only a numerical method would work. This is not an equation that would yield a closed form solution.
– Rebellos
Nov 19 at 6:03
Numerical schemes could be regula falsi or newton's method. However to which solution the scheme converges (and if it converges at all) is highly dependent on the starting values and the explicit values of $a,b,c,d$. Especially the value of $a$ is crucial for the behaviour.
– maxmilgram
Nov 19 at 6:36
1
1
Even when $a$ is a positive integer you cannot solve it explicitly.
– Kavi Rama Murthy
Nov 19 at 5:44
Even when $a$ is a positive integer you cannot solve it explicitly.
– Kavi Rama Murthy
Nov 19 at 5:44
@KaviRamaMurthy then, is there any way to get an approximated solution of $x$?
– kyub
Nov 19 at 5:52
@KaviRamaMurthy then, is there any way to get an approximated solution of $x$?
– kyub
Nov 19 at 5:52
Only a numerical method would work. This is not an equation that would yield a closed form solution.
– Rebellos
Nov 19 at 6:03
Only a numerical method would work. This is not an equation that would yield a closed form solution.
– Rebellos
Nov 19 at 6:03
Numerical schemes could be regula falsi or newton's method. However to which solution the scheme converges (and if it converges at all) is highly dependent on the starting values and the explicit values of $a,b,c,d$. Especially the value of $a$ is crucial for the behaviour.
– maxmilgram
Nov 19 at 6:36
Numerical schemes could be regula falsi or newton's method. However to which solution the scheme converges (and if it converges at all) is highly dependent on the starting values and the explicit values of $a,b,c,d$. Especially the value of $a$ is crucial for the behaviour.
– maxmilgram
Nov 19 at 6:36
add a comment |
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1
Even when $a$ is a positive integer you cannot solve it explicitly.
– Kavi Rama Murthy
Nov 19 at 5:44
@KaviRamaMurthy then, is there any way to get an approximated solution of $x$?
– kyub
Nov 19 at 5:52
Only a numerical method would work. This is not an equation that would yield a closed form solution.
– Rebellos
Nov 19 at 6:03
Numerical schemes could be regula falsi or newton's method. However to which solution the scheme converges (and if it converges at all) is highly dependent on the starting values and the explicit values of $a,b,c,d$. Especially the value of $a$ is crucial for the behaviour.
– maxmilgram
Nov 19 at 6:36