# 3^(x-1) + 25^(3x/2) = 15628

• Oct 2nd 2013, 05:48 PM
aldrincabrera
3^(x-1) + 25^(3x/2) = 15628
Good day...need ur help with this.. By trial and error, it is obvious that x=2. But how should we do this without using trial and error? That is, by any step by step method. If any. thanks
• Oct 2nd 2013, 07:28 PM
topsquark
Re: 3^(x-1) + 25^(3x/2) = 15628
Quote:

Originally Posted by aldrincabrera
Good day...need ur help with this.. By trial and error, it is obvious that x=2. But how should we do this without using trial and error? That is, by any step by step method. If any. thanks

Unless you have a typo and the RHS is supposed to be 15625 then x = 2 is not a solution....it's just very very close to 2. As far as I am aware there is no Algebraic method to solve this equation.

-Dan
• Oct 2nd 2013, 08:10 PM
votan
Re: 3^(x-1) + 25^(3x/2) = 15628
Quote:

Originally Posted by topsquark
Unless you have a typo and the RHS is supposed to be 15625 then x = 2 is not a solution....it's just very very close to 2. As far as I am aware there is no Algebraic method to solve this equation.

-Dan

I am still struggling with this one, wish me good luck, but x = 2 is exact: 3 + 25^3 = 15628
• Oct 2nd 2013, 08:24 PM
topsquark
Re: 3^(x-1) + 25^(3x/2) = 15628
Quote:

Originally Posted by votan
I am still struggling with this one, wish me good luck, but x = 2 is exact: 3 + 25^3 = 15628

(Ahem!) I forgot about the 3^(x - 1) term. Sorry!

Thanks for the catch.

-Dan
• Oct 2nd 2013, 08:54 PM
aldrincabrera
Re: 3^(x-1) + 25^(3x/2) = 15628
Hehehe, its okay.. i just dont know how to do this without trial and error
• Oct 16th 2013, 04:04 AM
aldrincabrera
Re: 3^(x-1) + 25^(3x/2) = 15628
• Oct 16th 2013, 04:52 AM
MINOANMAN
Re: 3^(x-1) + 25^(3x/2) = 15628
Aldrincambrera :
As Top squark mentioned above such kind of equations cannot be solved using algebraic methods...however:
transform the given equation into the form 3^x +3(125)^x =46884 then analyse the 46884 into the form 3^2+3(125)^2 and the solution x=2 is obvious.........
Have a good day.

In memory of my student Stefanos who died today ............may god bless his soul...........................
Minoas
• Oct 16th 2013, 04:53 AM
Prove It
Re: 3^(x-1) + 25^(3x/2) = 15628
You've already been told that there is not a way known to solve this equation exactly other than trial and error. If there are any other solutions you'll need to get approximations for them using numerical methods.
• Oct 16th 2013, 07:14 AM
WLX
Re: 3^(x-1) + 25^(3x/2) = 15628
3^(x-1)+25^(3/2x)=15628
3^(x-1)+(25^3/2)x=5^6 + 3
3^(x-1)+5^3x =5^6 + 3

x-1 =1 3x=6
x =2 x=2