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Logarithms Practice Test 1

Question : 1 of 40

Marks: +1, -0

\log_{10} 1\frac{1}{2} + \log_{10} 1\frac{1}{3} + \log_{10} 1\frac{1}{4} +

..... upto 198 terms?

Solution: 👈: Video Solution

Concept:

The sum of logarithms can be written as the logarithm of a product.

Explanation:

Write each term as a fraction:

\log_{10}\frac{3}{2}+\log_{10}\frac{4}{3}+\log_{10}\frac{5}{4}+\cdots+\log_{10}\frac{200}{199}

Combine them into one logarithm:

=\log_{10}\left(\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times\cdots\times\frac{200}{199}\right)

The product telescopes, so all middle terms cancel:

=\log_{10}\frac{200}{2}=\log_{10}100

Since

100=10^2

\log_{10}100=2\log_{10}10=2

Answer:

\boxed{2}

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