Question 112397
Given:
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{{{(1/2)^x = 4}}}
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Note that {{{1/2}}} is equivalent to {{{2^(-1)}}}
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This being the case, In the given equation you can replace {{{1/2}}} with {{{2^(-1)}}} and
when you do that the original equation becomes:
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{{{((2)^(-1))^x = 4}}}
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Then applying the power rule of exponents [the rule that says {{{(K^a)^b = K^(a*b)}}}]
you can reduce the equation by multiplying the two exponents -1 and x to get:
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{{{(2)^(-x) = 4}}}
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Now notice that the 4 on the right side is equivalent to {{{2^2}}}. Substitute this for 4
and the equation is then:
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{{{(2)^(-x) = 2^2}}}
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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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{{{-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}}}
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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 {{{1/D}}} by definition is {{{D^-1}}}.
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