SOLUTION: Solve for x: 3^(x+1) + 3^(x+2)=2916 I could get the answer by guessing, but I want to know the 'proper' way to solve this question. Thanks!

Algebra.Com
Question 1082548: Solve for x:
3^(x+1) + 3^(x+2)=2916
I could get the answer by guessing, but I want to know the 'proper' way to solve this question. Thanks!
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52864)   (Show Source): You can put this solution on YOUR website!
.
Your equation is the same as

 = 2916,

 = 2916,

 = 2916,

 =  = 243,

x = 5.

Solved.


Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!

Solve for x:
3^(x+1) + 3^(x+2)=2916
I could get the answer by guessing, but I want to know the 'proper' way to solve this question. Thanks!


 ------- Replacing 



a + 3a = 2,916 ---------- Substituting 

4a = 2,916



 ----- Re-substituting 

 ------ Converting 729 to base 3

x + 1 = 6 ---------- Bases are equal and so are their exponents

 

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