SOLUTION: Solve for x 3^(x+4)=27^(2x)

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Question 763120: Solve for x
3^(x+4)=27^(2x)
Found 3 solutions by Polyhymnio, MathLover1, DrBeeee:
Answer by Polyhymnio(2) About Me  (Show Source):
You can put this solution on YOUR website!
Since 27 = 3^3, we can rewrite the equation as
3^(x + 4) = 3^(6x)
Then take base 3 logarithms of both sides
x + 4 = 6x
5x = 4
x = 4/5

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

3%5E%28x%2B4%29=27%5E%282x%29.......since 27%5E%282x%29=%283%5E3%29%5E%282x%29=3%5E%286x%29, we have

3%5E%28x%2B4%29=3%5E%286x%29...if bases equal then exponents have to be equal too
so, we will have
x%2B4=6x...solve for x
4=6x-x
4=5x
4%2F5=x

Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given
(1) 3%5E%28x%2B4%29+=+27%5E%282x%29
Now we know that
(2) 27+=+3%5E3 and apply the rule that when we raise a power by an exponent, we multiply the exponents.
For example,
(3) %28a%5Eb%29%5Ec+=+a%5E%28b%2Ac%29
In our case we have
(4) 3%5E%28x%2B4%29+=+%283%5E3%29%5E%282%2Ax%29 or
(5) 3%5E%28x%2B4%29+=+3%5E%283%5E%282%2Ax%29%29+ or
(6) 3%5E%28x%2B4%29+=+3%5E%286%2Ax%29
Now the powers have equal bases on the both sides of (6), so we can equate the exponents and get
(7) x + 4 = 6x or
(8) x = 4/5