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

Step 1: Find \( \log20 \) via \( 20=4\times5 \): \[ \log20=\log4+\log5=2\log2+(1-\log2)=1+\log2=1+0.3=1.3. \]

Step 2: Each term converts as \( \log_{20}10^k=\dfrac{k}{1.3} \), so the sum is \[ \frac{2+3+4}{1.3}=\frac{9}{1.3}. \]
\[ \boxed{\frac{90}{13}} \]