Question

If $\log _{10} 2= a , \log _{10} 3= b$ then $\log _{0.72}(9.6)$ in terms of $a$ and $b$ is equal to

• A. $\frac{2 a+3 b-1}{5 a+b-2}$
• B. $\frac{5 a+b-1}{3 a+2 b-2}$
• C. $\frac{3 a+b-2}{2 a+3 b-1}$
• D. $\frac{2 a+5 b-2}{3 a+b-1}$

Answer 1

Answer: (B)

$\log _{0.72}(9.6)=\log _{\frac{72}{100}}\left(\frac{96}{10}\right)=\frac{\left(\log _{10} 96-\log _{10} 10\right)}{\left(\log _{10} 72-\log _{10} 100\right)} $
$=\frac{\log _{10}\left(2^5 \times 3\right)-1}{\log _{10}\left(2^3 \times 3^2\right)-2}=\left(\frac{5 a+b-1}{3 a+2 b-2}\right) $