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 ->  Expressions -> 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!      Log On


   

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(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.
Your equation is the same as

3%2A3%5Ex+%2B+9%2A3%5Ex = 2916,

%283%2B9%29%2A3%5Ex = 2916,

12%2A3%5Ex = 2916,

3%5Ex = 2916%2F12 = 243,

x = 5.

Solved.


Answer by MathTherapy(10555) About Me  (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!
matrix%281%2C3%2C+3%5E%28x+%2B+1%29+%2B+3%5E%28x+%2B+2%29%2C+%22=%22%2C+%222%2C916%22%29

 ------- Replacing matrix%281%2C3%2C+3%5E%28x+%2B+2%29%2C+with%2C+%283%5E1%29%283%5E%28x+%2B+1%29%29%29



a + 3a = 2,916 ---------- Substituting matrix%281%2C3%2C+a%2C+for%2C+3%5E%28x+%2B+1%29%29

4a = 2,916

matrix%281%2C5%2C+a%2C+%22=%22%2C+%222%2C916%22%2F4%2C+%22=%22%2C+729%29

matrix%281%2C3%2C+3%5E%28x+%2B+1%29%2C+%22=%22%2C+729%29 ----- Re-substituting matrix%281%2C5%2C+a%2C+%22=%22%2C+729%2C+for%2C+3%5E%28x+%2B+1%29%29

matrix%281%2C3%2C+3%5E%28x+%2B+1%29%2C+%22=%22%2C+3%5E6%29 ------ Converting 729 to base 3

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

highlight_green%28matrix%281%2C5%2C+x%2C+%22=%22%2C+6+-+1%2C+%22=%22%2C+5%29%29