Logarithms Practice Test 1

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What is the value of:

\log_10 1 1/2+\log_10 1 1/3+\log_10 1 1/4+

..... upto 198 terms?

Solution:

\log_10 1 1/2+\log_10 1 1/3+\log_10 1 1/4+

..... upto 198 terms

\log_10 3/2+\log_10 4/3+\log_10 5/4+...+\log_10 199/198+\log_10 200/199

=\log_10(3/2×4/3×5/4×...×199/198×200/199)

=\log_10 200/2=\log_10 100

=2\log_10 10=2×1=2

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