SOLUTION: Thank you in advance for helping me double check this problem. 27^4x=9^x+1 this is what I got...1/10????

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Thank you in advance for helping me double check this problem. 27^4x=9^x+1 this is what I got...1/10????      Log On


   

Question 176824This question is from textbook college algebras
: Thank you in advance for helping me double check this problem.
27^4x=9^x+1
this is what I got...1/10???? This question is from textbook college algebras

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
27%5E%284x%29+=+9%5E%28x%2B1%29 Start with the given equation.


%283%5E3%29%5E%284x%29+=+%283%5E2%29%5E%28x%2B1%29 Rewrite 27 as 3%5E3. Rewrite 9 as 3%5E2.


3%5E%2812x%29+=+3%5E%282%28x%2B1%29%29 Multiply the exponents.


Since the bases are equal, the exponents are equal.


12x=2%28x%2B1%29 Set the exponents equal to one another.


12x=2x%2B2 Distribute.


12x-2x=2 Subtract 2x from both sides.


10x=2 Combine like terms on the left side.


x=%282%29%2F%2810%29 Divide both sides by 10 to isolate x.


x=1%2F5 Reduce.


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Answer:

So the answer is x=1%2F5