Question

Find the value of  $\log_{20} 100 + \log_{20} 1000 + \log_{20} 10000 \quad \bigl[\textit{Assume that } \log 2 = 0.3\bigr].$ 
 

• A. $90/13$
• B. $80/13$
• C. $110/13$
• D. $70/13$

Hint:

For $\log_a b$ with common logs, use $\log_a b=\frac{\log b}{\log a}$. Precompute $\log a$ once.

Answer 1

The Correct Option is A

Use change of base: $\log_{20}N=\dfrac{\log N}{\log 20}$. Since $\log 20=\log(2\cdot 10)=\log 2+1=1.3$, \[ \log_{20}100+\log_{20}1000+\log_{20}10000 =\frac{2+3+4}{1.3} =\frac{9}{1.3}=\frac{90}{13}. \]