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
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-> 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
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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
You can put this solution on YOUR website! Given:
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Note that is equivalent to
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This being the case, In the given equation you can replace with and
when you do that the original equation becomes:
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Then applying the power rule of exponents [the rule that says ]
you can reduce the equation by multiplying the two exponents -1 and x to get:
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Now notice that the 4 on the right side is equivalent to . Substitute this for 4
and the equation is then:
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Now the bases are the same so the exponents must be equal. Setting the exponents equal results in:
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Solve for x by multiplying both sides of this equation by -1 to convert it to:
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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 by definition is .
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