SOLUTION: I have been struggling on this problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Using Laws of Exponents solve for n.

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Question 163874This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been struggling on this problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!
Using Laws of Exponents
solve for n.
4^n+3*16^n=8^3n This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Assume the problems is:
:
4%5E%28n%2B3%29%2A16%5En= 8%5E%283n%29
:
note all these values are powers of 2, 4=2^2; 16 = 2^4; 8 = 2^3
so we can write this equation:
2%5E%282%28n%2B3%29%29%2A2%5E%284n%29= 2%5E%283%283n%29%29
which is:
2%5E%282n%2B6%29%2A2%5E%284n%29= 2%5E%289n%29
Which is:
2%5E%282n%2B6%2B4n%29= 2%5E%289n%29
2%5E%286n%2B6%29= 2%5E%289n%29
Therefore we can say
6n + 6 = 9n
6 = 9n - 6n
6 = 3n
n = 6%2F3
n = 2
;
;
Substitute for n in the original equation and enter in a good calc to prove it