solving exponential function with linear function
0
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 '18 at 5:42
kyub
375
add a comment |
0
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 '18 at 5:42
kyub
375
1
Even when $a$ is a positive integer you cannot solve it explicitly.
– Kavi Rama Murthy
Nov 19 '18 at 5:44
@KaviRamaMurthy then, is there any way to get an approximated solution of $x$?
– kyub
Nov 19 '18 at 5:52
Only a numerical method would work. This is not an equation that would yield a closed form solution.
– Rebellos
Nov 19 '18 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 '18 at 6:36
add a comment |
0
0
0
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 '18 at 5:42
kyub
375
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 '18 at 5:42
kyub
375
asked Nov 19 '18 at 5:42
kyub
375
asked Nov 19 '18 at 5:42
kyub
375
asked Nov 19 '18 at 5:42
kyub
375
asked Nov 19 '18 at 5:42
kyub
375
375
1
Even when $a$ is a positive integer you cannot solve it explicitly.
– Kavi Rama Murthy
Nov 19 '18 at 5:44
@KaviRamaMurthy then, is there any way to get an approximated solution of $x$?
– kyub
Nov 19 '18 at 5:52
Only a numerical method would work. This is not an equation that would yield a closed form solution.
– Rebellos
Nov 19 '18 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 '18 at 6:36
add a comment |
1
Even when $a$ is a positive integer you cannot solve it explicitly.
– Kavi Rama Murthy
Nov 19 '18 at 5:44
@KaviRamaMurthy then, is there any way to get an approximated solution of $x$?
– kyub
Nov 19 '18 at 5:52
Only a numerical method would work. This is not an equation that would yield a closed form solution.
– Rebellos
Nov 19 '18 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 '18 at 6:36
1
1
Even when $a$ is a positive integer you cannot solve it explicitly.
– Kavi Rama Murthy
Nov 19 '18 at 5:44
Even when $a$ is a positive integer you cannot solve it explicitly.
– Kavi Rama Murthy
Nov 19 '18 at 5:44
@KaviRamaMurthy then, is there any way to get an approximated solution of $x$?
– kyub
Nov 19 '18 at 5:52
@KaviRamaMurthy then, is there any way to get an approximated solution of $x$?
– kyub
Nov 19 '18 at 5:52
Only a numerical method would work. This is not an equation that would yield a closed form solution.
– Rebellos
Nov 19 '18 at 6:03
Only a numerical method would work. This is not an equation that would yield a closed form solution.
– Rebellos
Nov 19 '18 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 '18 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 '18 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 '18 at 5:44
@KaviRamaMurthy then, is there any way to get an approximated solution of $x$?
– kyub
Nov 19 '18 at 5:52
Only a numerical method would work. This is not an equation that would yield a closed form solution.
– Rebellos
Nov 19 '18 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 '18 at 6:36