SOLUTION: Solve x in the following exponential notation {{{9^(2x+1)=243}}}

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Question 641766: Solve x in the following exponential notation 9%5E%282x%2B1%29=243
Found 3 solutions by Earlsdon, MathLover1, DrBeeee:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
9%5E%282x%2B1%29+=+243 Find the common base.
%283%5E2%29%5E%282x%2B1%29+=+3%5E5 Simplify.
3%5E%284x%2B2%29+=+3%5E5 The bases are equal so the exponents are equal.
4x%2B2+=+5
4x+=+3
x+=+3%2F4

Answer by MathLover1(20849) About Me  (Show Source):
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Since 9 = 3^2, 9^(2x+1) is
(1) LS = 3^(4x+2)
and
(2) RS = 243 = 3^5
Equating (1) and (2) we have
(3) 3^(4x+2) = 3^5,
Since the bases are equal we can equate the exponents and obtain
(4) 4x + 2 = 5 or
(5) 4x = 3 or
(6) x = 3/4
Check your answer
Is (9^(2*(3/4)+1) = 243)?
Is (9^(10/4) = 243)?
Is (9^(5/2) = 243)?
Is ((9^(1/2))^5 = 243)?
Is (3^5 = 243)?
Is (243 = 243)? Yes
Answer is x = 3/4