InterviewSolution
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InterviewSolution
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Solve the equation `5^(x)root(x)(8^(x-1))=500` |
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Answer» We have `5^(x)root(x)(8^(x-1))=5^(3).2^(2)` `implies5^(x).7^(((x-1)/3))=5^(3).2^(2)` `implies5^(x).2^((3x-3)/x)=5^(3).2^(2)` `implies5^(x_3).2(((x-3)/x))=1` `implies(5.2^(1//x)(x-3))=1` is equivalent to the equation `10^((x-3)log5.2^(1//x))=1` `implies(x-3)log(5.2^(1//x))=0` Thus, original equation is equivalent to the collection of equations `x-3=0,log(5.2^(1//x))=0` `:.x_(1)=3,5.2^(1//x)=1implies2^(1//x)=(1/5)` `:.x_(2)=-log_(5)2` Hence roots of the original equation are `x_(1)=3` and `x_(2)=-log_(5)2`. |
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