Question

Which of the following numbers is/are positive?

• A. $\ln 2+\ln 3+\ln 0.161$
• B. $\ln 3+\ln (1.4)-\frac{1}{2} \ln 16$
• C. $1+2 \log _{10} 3-3 \log _{10} 5+\log _{10} 5$
• D. $\log _{\frac{1}{2}}\left(\frac{1}{3}\right)-\log _{\frac{1}{3}}\left(\frac{1}{2}\right)$

Answer 1

Answer: (B), (C), (D)

(A) $ \ln \frac{6 \times 161}{1000}=\ln \frac{966}{1000}=\ln 0.966=- ve$
(B) $ \ln \left(\frac{(3)(1.4)}{4}\right)=\ln \left(\frac{4 \cdot 2}{4}\right)=+ ve$
(C) $\log \left(\frac{90 \times 5}{125}\right)=\log \left(\frac{18}{5}\right)=+ ve$
(D) $\log _2 3-\log _3 2=+$ ve