SOLUTION: Please help me solve for n. I don't know where to begin. 3 x 9^2n = {3^(n+1)}^3

Algebra ->  Exponents -> SOLUTION: Please help me solve for n. I don't know where to begin. 3 x 9^2n = {3^(n+1)}^3      Log On


   

Question 654100: Please help me solve for n. I don't know where to begin.
3 x 9^2n = {3^(n+1)}^3
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

recall:
the first basic exponent rule: Whenever you multiply two terms with the same base, you can add the exponents:
%28+x%5E+m+%29+%28+x%5E+n+%29+=+x%5E%28+m+%2B+n+%29

3%2A9%5E%282n%29+=+%283%5E%28n%2B1%29%29%5E3

3%2A%283%5E2%29%5E%282n%29+=+3%5E%283n%2B3%29

3%5E1%2A3%5E%282%2A2n%29+=+3%5E%283n%2B3%29

3%5E%284n%2B1%29+=+3%5E%283n%2B3%29.... if bases same, exponents are same too
so, we have

4n%2B1+=+3n%2B3....solve for n
4n-3n+=+3-1
highlight%28n+=+2%29