Question 95

Find the value of $$\log_{10}{10} + \log_{10}{10^2} + ..... + \log_{10}{10^n}$$

Solution

$$\log_{10}{10} + \log_{10}{10^2} + ..... + \log_{10}{10^n}$$

Since $$\log_aa\ $$ = 1

$$\log_{10}{10} + \log_{10}{10^2} + ..... + \log_{10}{10^n}$$ = 1+2+....n

=$$\ \frac{\ n\left(n+1\right)}{2}$$ 

=$$\frac{(n^{2} + n)}{2}$$

D is the correct answer.

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