Question

If ${\log }_{10}2=a$ and ${\log }_{10}3=b$, then express $\log 5.4$ in terms of $a$ and $b$

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

Answer 1

Answer: (D)

$a+3b-1$

${\log }_{10}2=a{\log }_{10}3=b\log 5.4=\log \left(\frac{54}{10}\right)=\log \left(\frac{{2\times 3}^3}{10}\right)=\log 2+3\log 3-\log 10=\log 2+3\log 3-1=a+3b-1$