Solve:2log2(log2x)+ log1/2(log22root2x) =1

Asked by Anil | 5th May, 2017, 12:50: PM

Expert Answer:

begin mathsize 16px style 2 log subscript 2 left parenthesis log subscript 2 straight x right parenthesis plus space log subscript 1 divided by 2 end subscript left parenthesis log subscript 2 2 root 2 straight x right parenthesis space equals 1
Put space straight x equals 2 to the power of straight y
rightwards double arrow 2 log subscript 2 left parenthesis straight y right parenthesis plus space log subscript 1 divided by 2 end subscript left parenthesis log subscript 2 2 open square brackets 2 cross times 2 to the power of straight y close square brackets to the power of 1 half end exponent right parenthesis space equals 1
rightwards double arrow 2 log subscript 2 left parenthesis straight y right parenthesis plus space log subscript 1 divided by 2 end subscript left parenthesis log subscript 2 2 to the power of fraction numerator straight y plus 3 over denominator 2 end fraction end exponent right parenthesis space equals 1 space
rightwards double arrow 2 log subscript 2 left parenthesis straight y right parenthesis minus space log subscript 2 left parenthesis log subscript 2 2 to the power of fraction numerator straight y plus 3 over denominator 2 end fraction end exponent right parenthesis space equals 1 space
rightwards double arrow log subscript 2 left parenthesis straight y right parenthesis squared minus log subscript 2 left parenthesis fraction numerator straight y plus 3 over denominator 2 end fraction right parenthesis space equals 1
rightwards double arrow log subscript 2 open parentheses fraction numerator straight y squared over denominator fraction numerator straight y plus 3 over denominator 2 end fraction end fraction close parentheses equals 1
rightwards double arrow fraction numerator straight y squared over denominator fraction numerator straight y plus 3 over denominator 2 end fraction end fraction equals 2
rightwards double arrow straight y squared equals straight y plus 3
rightwards double arrow straight y squared minus straight y minus 3 equals 0
Solving space quadratic space equation space using space formula space you space will space get space
straight y equals fraction numerator 1 plus-or-minus square root of 13 over denominator 2 end fraction rightwards double arrow straight x equals 2 to the power of open parentheses fraction numerator 1 plus-or-minus square root of 13 over denominator 2 end fraction close parentheses end exponent

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Answered by Sneha shidid | 8th May, 2017, 09:06: AM