SOLUTION: Our lesson on rational exponents is asking for us to solve for x here; 4^(x+1)=1/4 Please help me find the answer. Thanks.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Our lesson on rational exponents is asking for us to solve for x here; 4^(x+1)=1/4 Please help me find the answer. Thanks.      Log On


   

Question 1093274: Our lesson on rational exponents is asking for us to solve for x here;
4^(x+1)=1/4
Please help me find the answer. Thanks.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
If you want to write 4%5E%28x%2B1%29=1%2F4 you must write

4^(x+1)=1/4, not 4^x+1=1/4, for that means 4%5Ex%2B1=1%2F4.

When you must type mathematics all on one line, you must
always enclose in parentheses what is understood to be
above or below the line if it contains more than one number 
or letter.

4%5E%28x%2B1%29=1%2F4

We write 1%2F4 as 4%5E%28-1%29, then we have

4%5E%28x%2B1%29=4%5E%28-1%29

And we use the principle that the equation B%5EA=B%5EC is
equivalent to the equation A=C if the base B is positive
and different from 1.

Since the base 4 is positive and not equal to 1, the equation
is equivalent to

x%2B1=-1

So

x=-2

Checking in the original:

4%5E%28x%2B1%29=1%2F4

4%5E%28-2%2B1%29=1%2F4

4%5E%28-1%29=1%2F4

1%2F4=1%2F4

Edwin