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27^x =  √3 x 9^(x+2)

 Sep 16, 2018
 #1
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Solve for x:
27^x = 3^(2 x + 9/2)

Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):
3 log(3) x = log(3) (2 x + 9/2)

Divide both sides by log(3):
3 x = 2 x + 9/2

Subtract 2 x from both sides:
x = 9/2

 Sep 16, 2018

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