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CBSE Class 11-science Answered

fraction numerator log subscript 8 17 over denominator log subscript 9 space 23 end fraction minus fraction numerator log subscript 2 square root of 2 end subscript space 17 over denominator log subscript 3 space 23 end fraction
Asked by devinpatel93 | 14 Oct, 2020, 06:01: PM
answered-by-expert Expert Answer
Let us use the logarithm base change rule
 
begin mathsize 16px style log subscript b a space equals space fraction numerator log subscript x a over denominator log subscript x b end fraction end style
begin mathsize 16px style fraction numerator log subscript 8 17 over denominator log subscript 9 23 end fraction space minus space fraction numerator log subscript 2 square root of 2 end subscript 17 over denominator log subscript 3 23 end fraction space equals space fraction numerator log subscript 10 17 over denominator log subscript 10 8 end fraction cross times fraction numerator log subscript 10 9 over denominator log subscript 10 23 end fraction space minus space fraction numerator log subscript 10 17 over denominator log subscript 10 2 square root of 2 end fraction cross times fraction numerator log subscript 10 3 over denominator log subscript 10 23 end fraction end style  .......................(1)
let us consider begin mathsize 16px style log subscript 10 9 space equals space 2 space log subscript 10 3 end style  and  begin mathsize 16px style log subscript 10 8 space equals space 2 space log subscript 10 2 square root of 2 end style
Hence eqn.(1) is rewritten as 
 
begin mathsize 16px style fraction numerator log subscript 8 17 over denominator log subscript 9 23 end fraction space minus space fraction numerator log subscript 2 square root of 2 end subscript 17 over denominator log subscript 3 23 end fraction space equals space fraction numerator log subscript 10 17 over denominator log subscript 10 2 square root of 2 end fraction cross times fraction numerator log subscript 10 3 over denominator log subscript 10 23 end fraction space open curly brackets 2 over 2 space minus space 1 close curly brackets space equals space 0 end style
Answered by Thiyagarajan K | 14 Oct, 2020, 07:14: PM

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