Question:
1/log2100-1/log4100+1/log5100-1/log10100+1/log20100-1/log25100+1/log50100=?
1/log2100-1/log4100+1/log5100-1/log10100+1/log20100-1/log25100+1/log50100=?
Updated On: Sep 30, 2024
- \(\frac 12\)
- 0
- 10
- -4
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The Correct Option is A
Solution and Explanation
The correct answer is (A):
We know that 1/logba = logab, therefore,
1/log2100-1/log4100+1/log5100-1/log10100+1/log20100-1/log25100+1/log50100
= log100 2-log100 4+ log100 5-log100 10+log100 20-log100 25+log100 50
= log100(2/4×5/10×20/25×50)
= log10010
Using the relation log amb = 1/m logab
log100 10 = log10210 = 1/2 log10 10 = 1/2
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