Question

If $a^4.b^5=1$, then the value of ${\log }_a\left(a^5{b}^4\right)$ will be

• A. $\frac{9}{5}$
• B. $4$
• C. $5$
• D. $\frac{8}{5}$

Answer 1

The correct option is A $\frac{9}{5}$

We have, $a^4\cdot b^5=1$
$\Rightarrow b^5=a^{-4}\Rightarrow b=a^{-4/5}$
$\therefore {\log }_a\left(a^5{b}^4\right)={\log }_a(a^5\cdot a^{4(-4/5)})$
$={\log }_a\left(a^{5-16/5}\right)={\log }_a{a}^{9/5}=\frac{9}{5}{\log }_{a}a=\frac{9}{5},\because {\log }_{a}a=1$