Question

If ${\log }_{a}b=2$ and ${\log }_{a}c=3$, then the value of $\frac{c}{ab}$ is equal to

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

Given that ${\log }_{a}b=2$
And ${\log }_{a}c=3$
Consider, ${\log }_a\left(\frac{c}{ab}\right)={\log }_{a}c-{\log }_{a}a-{\log }_{a}b=3-1-2=0,[\because \log \frac{a}{b}=\log a-\log b,{\log }_{a}a=1]$
$\Rightarrow \frac{c}{ab}=a^0=1$
Ans: 1