SOLUTION: I have an assignment what's due Monday and the question says, Solve the following equation: {{{ 4^(x+1) = 16^x }}} I know you have to do something about letting them both have

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Question 1069001: I have an assignment what's due Monday and the question says, Solve the following equation:
I know you have to do something about letting them both have the same base, but I don't know what to do after that.
Please Help and Thank you!

Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
Write both of them to the same base, 2 or 4, 4 is easier
4^(x+1)=(4^2)^x=4^2x
now you have the same base, so you can set the exponents equal to each other.
x+1=2x
x=1
4^2=16^1

Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
Let us write the right side in the base 4:


 =  = .


Now the equation takes the form


 = .


It implies 


x + 1 = 2x  --->  x = 1.


Answer.  x = 1.


Check.  Left side is  =  = 16.

        Right side of the original equation is  =  = 16.

        Checked.

Solved.


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