Question

If ${\log }_{10}2=a$ and ${\log }_{10}3=b$, then $\log 5.4$ can be expressed as

• A. $a-3b-1$
• B. $a+3b+1$
• C. $a+3b-1$
• D. $a-3b+1$

Answer 1

Answer: (C)

$a+3b-1$

$x=\log 5.4$
$\therefore x=\log \frac{27}{5}$
$\therefore x=\log 3^3-\log \frac{10}{2}$ ....$(\log \frac{a}{b}=\log a-\log b)$
$\therefore x=3\log 3-(\log 10-\log 2)$ ....$\log a^b=b\log a$
$\therefore x=3b-1+a$