SOLUTION: the problem is- (1/2) raised to the x and it is equal to 4. first thing i know we have to do is, to set the bases equal, but since this is a fraction, i'm not quite sure on how to

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: the problem is- (1/2) raised to the x and it is equal to 4. first thing i know we have to do is, to set the bases equal, but since this is a fraction, i'm not quite sure on how to      Log On


   



Question 112397This question is from textbook A graphical Approach to College Algebra
: the problem is- (1/2) raised to the x and it is equal to 4. first thing i know we have to do is, to set the bases equal, but since this is a fraction, i'm not quite sure on how to get there. which is what i need help on...is how to find the same base for this problem since it is a fraction! This question is from textbook A graphical Approach to College Algebra

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
%281%2F2%29%5Ex+=+4
.
Note that 1%2F2 is equivalent to 2%5E%28-1%29
.
This being the case, In the given equation you can replace 1%2F2 with 2%5E%28-1%29 and
when you do that the original equation becomes:
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%28%282%29%5E%28-1%29%29%5Ex+=+4
.
Then applying the power rule of exponents [the rule that says %28K%5Ea%29%5Eb+=+K%5E%28a%2Ab%29]
you can reduce the equation by multiplying the two exponents -1 and x to get:
.
%282%29%5E%28-x%29+=+4
.
Now notice that the 4 on the right side is equivalent to 2%5E2. Substitute this for 4
and the equation is then:
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%282%29%5E%28-x%29+=+2%5E2
.
Now the bases are the same so the exponents must be equal. Setting the exponents equal results in:
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-x+=+2
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Solve for x by multiplying both sides of this equation by -1 to convert it to:
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x+=+-2
.
Hope this makes sense to you and helps you to see your way through the problem. The key to
solving this problem was to recognize that 1%2FD by definition is D%5E-1.
.