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ICSE Class 9 Answered

Q2.
Asked by sksraghav67 | 07 Jul, 2022, 08:12: PM
Expert Answer
Given colon space straight x equals open parentheses 2 to the power of square root of 5 end exponent close parentheses open parentheses 5 to the power of square root of 2 end exponent close parentheses
Now comma space
log subscript 10 straight x
equals log subscript 10 open square brackets open parentheses 2 to the power of square root of 5 end exponent close parentheses open parentheses 5 to the power of square root of 2 end exponent close parentheses close square brackets
equals log subscript 10 open parentheses 2 to the power of square root of 5 end exponent close parentheses plus log subscript 10 open parentheses 5 to the power of square root of 2 end exponent close parentheses
equals square root of 5 space log subscript 10 2 space plus space square root of 2 space log subscript 10 5
equals square root of 5 space log subscript 10 2 space plus space square root of 2 space log subscript 10 open parentheses 10 over 2 close parentheses
equals square root of 5 space log subscript 10 2 space plus space square root of 2 space open parentheses log subscript 10 10 minus log subscript 10 2 close parentheses
equals square root of 5 space log subscript 10 2 space plus space square root of 2 space open parentheses 1 minus log subscript 10 2 close parentheses
equals square root of 5 space log subscript 10 2 space plus space square root of 2 minus space square root of 2 space log subscript 10 2
equals open parentheses square root of 5 minus square root of 2 close parentheses log subscript 10 2 plus square root of 2
As space it space is space given space that comma space log subscript 10 straight x equals open parentheses square root of straight A minus square root of straight B close parentheses open parentheses log subscript 10 2 close parentheses plus square root of straight B
Thus comma space open parentheses square root of 5 minus square root of 2 close parentheses log subscript 10 2 plus square root of 2 equals open parentheses square root of straight A minus square root of straight B close parentheses open parentheses log subscript 10 2 close parentheses plus square root of straight B
rightwards double arrow straight A equals 5 space and space straight B equals 2
Hence comma space straight A plus straight B equals 7
Answered by Renu Varma | 08 Jul, 2022, 05:08: PM

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