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

Question 763120: Solve for x
3^(x+4)=27^(2x)
Found 3 solutions by Polyhymnio, MathLover1, DrBeeee:
Answer by Polyhymnio(2)   (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)   (Show Source): You can put this solution on YOUR website!

.......since , we have

...if bases equal then exponents have to be equal too
so, we will have
...solve for

Answer by DrBeeee(684)   (Show Source): You can put this solution on YOUR website!
Given
(1)
Now we know that
(2) and apply the rule that when we raise a power by an exponent, we multiply the exponents.
For example,
(3)
In our case we have
(4) or
(5) or
(6)
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
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