SOLUTION: I think I have to solve it using the log functions not sure the problem reads... solve equation 9^(x+3)=3^(4x-2) if not I got x=4 but that just by using guessing. I need to kn

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I think I have to solve it using the log functions not sure the problem reads... solve equation 9^(x+3)=3^(4x-2) if not I got x=4 but that just by using guessing. I need to kn      Log On


   

Question 752775: I think I have to solve it using the log functions not sure
the problem reads...
solve equation 9^(x+3)=3^(4x-2)
if not I got x=4
but that just by using guessing.
I need to know how I get there using logs or if I do have to use them.
Found 2 solutions by Edwin McCravy, ankor@dixie-net.com:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
9x+3 = 34x-2

Write 9 as 32

(32)x+3 = 34x-2

Multiply the exponent 2 of the base 3 inside the 
parentheses times the exponent x+3.

32(x+3) = 34x-2

Since the bases are the same, 3,  on both sides 
of the equation, the exponents must be equal:

2(x+3) = 4x-2
  2x+6 = 4x-2
   -2x = -8
     x = 4

That's the way you get the answer 4 without
guessing and checking.     

Edwin

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
solve equation 9^(x+3)=3^(4x-2)
We know that 9 = 3^2, therefore we can write the equation as
3%5E%282%28x%2B3%29%29 = 3%5E%28%284x-2%29%29
When the numbers are equal, the exponents are equal, so we have:
2(x+3) = 4x -2
2x + 6 = 4x - 2
6 + 2 = 4x - 2x
8 = 2x
x = 8/2
x = 4