Solving x * a^x

[Pepehands]

Hello, I hope I posted this thread in the right category.

I'm having troubles solving an equation of the form of :
[imath](k+x)*a^x[/imath]
k and a being constants

Individually, I know how to solve [imath]k*a^x[/imath], but I have no clue for that other part [imath]x * a^x[/imath]

With the two together I don't even know where I should start, or where I could find information that would help me

Thanks in advance for any advice you may have !

 

[Deleted member 4993]

Hello, I hope I posted this thread in the right category.

I'm having troubles solving an equation of the form of :
[imath](k+x)*a^x[/imath]
k and a being constants

Individually, I know how to solve [imath]k*a^x[/imath], but I have no clue for that other part [imath]x * a^x[/imath]

With the two together I don't even know where I should start, or where I could find information that would help me

Thanks in advance for any advice you may have !

Please post the complete and EXACT problem as it was presented to you.

In the problem statement in your post, you do NOT have an "equation" to solve! There is no "=" sign in there .

 

[Pepehands]

I kinda forgot the y part, my bad !
I'm trying to make a program that finds the value of x for the given 'k' and 'a' and 'y' constants.
So I'm the one who put the equation together.

So the equation I want to solve is :
[imath](k*y + x)*a^x = y[/imath]

As for an example of one I solved 'manually', with k =0.5, x =1.01 and y = 6750 :
[imath](3375+x)*1.01^x = 6750[/imath]
I want to be able to find 67 or 68 (basically on of the nearing integer)

 

[Deleted member 4993]

I kinda forgot the y part, my bad !
I'm trying to make a program that finds the value of x for the given 'k' and 'a' and 'y' constants.
So I'm the one who put the equation together.

So the equation I want to solve is :
[imath](k*y + x)*a^x = y[/imath]

As for an example of one I solved 'manually', with k =0.5, x =1.01 and y = 6750 :
[imath](3375+x)*1.01^x = 6750[/imath]
I want to be able to find 67 or 68 (basically on of the nearing integer)

(k + x) * a^x = B cannot be solved, for unknown constants , using simple algebraic method.

The solution can be approximated for given values, through iterations, using numerical methods - e.g. Newton's method. Have you been taught that method ?

 

[Pepehands]

Thanks a lot for your answer !

After watching a quick video on it, I actually remember doing one exercise on that in my schooling a long time ago, so I should be fine !
I now remember my teacher saying that he wasn't too fond of these kind of approximation exercises

I wanted to know if there was some math that would give me the result without having to iterate, iteration being my first idea to solve that issue.

I wanted to be sure there wasn't a simple way to find the result, as I know I will need lots of iteration to find my result.
(My 'a' constant being very close to 1, and my 'y' constant that could reach high values like 10^15

Now I know what I need to go for, thanks again !

 

[Deleted member 4993]

I wanted to be sure there wasn't a simple way to find the result, as I know I will need lots of iteration to find my result.
(My 'a' constant being very close to 1, and my 'y' constant that could reach high values like 10^15

The Newton-Raphson method converges real fast for most of the practical problems.

my teacher saying that he wasn't too fond of these kind of approximation exercises

However, >90% of the practical problems do not have "closed-form" algebraic solution and need t be approximated through numerical-iterations.