Question

If ${\log }_{x}2=a,{\log }_{x}3=b,{\log }_{x}5=c$ then find the value of the following in terms of $a,b$ and $c$
(i) ${\log }_{x}16$ (ii) ${\log }_{x}75$ (iii) ${\log }_{x}60$

• A. $4a,2a+b,2a+b+c$
• B. $4a,2c+b,2a+b+c$
• C. $4a,2c+b,2c+b+a$
• D. $4a,2c+b,2a+3b+c$

Answer 1

The correct option is B $4a,2c+b,2a+b+c$

${\log }_{x}2=a;{\log }_{x}3=b;{\log }_{x}5=c$

$i){\log }_{x}16={\log }_x{2}^4=4{\log }_{x}2=4a$

$ii){\log }_{x}75={\log }_{x}3\times 5^2={\log }_{x}3+{\log }_x{5}^2=b+2c$

$iii){\log }_{x}60={\log }_x{2}^2+{\log }_{x}3+{\log }_{x}5=2a+b+c$