Question

If ${\log }_{30}3=c$ and ${\log }_{30}5=d$, then the value of ${\log }_{30}8$ is

• A. $2(1-c-d)$
• B. $3(1+c+d)$
• C. $3(1+c-d)$
• D. $3(1-c-d)$

Answer 1

The correct option is D $3(1-c-d)$

Given that, ${\log }_{30}3=c,{\log }_{30}5=d$
${\log }_{30}8={\log }_{30}{2}^3=3{\log }_{30}2[\because \log a^m=m\log a]=3{\log }_{30}\frac{30}{15}$
$\Rightarrow {\log }_{30}8=3({\log }_{30}30-{\log }_{30}3-{\log }_{30}5),[\because \log \frac{a}{b}=\log a-\log b\text{\&}\log (ab)=\log a+\log b]$
$\Rightarrow {\log }_{30}8=3(1-c-d)$
Ans: D