Question

Log10(1 + 1/2) + log10(1 + 1/3) + log10 (1 + 1/4) + ......log10 (1+ 1/1999) when simplified has the value equal

Answer 1

Answer:

1. the answer is 1

Step-by-step explanation:

Answer 2

The simplified value is 3.

Given:

Log10(1 + 1/2) + log10(1 + 1/3) + log10 (1 + 1/4) + ......log10 (1+ 1/1999)

To find:

The simplified value

Solution:

We can obtain the required value by using the following property.

$log_{a}b +log_{a}c =log_{a}bc$

The given expression can be written as follows.

$log_{10}$ (3/2)+ $log_{10}$ (4/3)+ $log_{10}$ (5/4) and so on till $log_{10}$ (2000/1999).

= $log_{10}$ (3/2×4/3×5/4×6/5×...×2000/1999)

= $log_{10}$ (2000/2)

= $log_{10}$ 1000

=$log_{10}$ $10^{3}$

Now, we know that $log_{10} 10^{3}=3 log_{10} 10$ and $log_{10} 10=1$.

=3 $log_{10}$ 10

=3×1

=3

Therefore, the simplified value is 3.

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