Question

If ${\log }_b\left(a\right)=x$ and ${\log }_b\left(c\right)=y$, and $4x+6y=8$, then ${\log }_b(a^2.c^3)$

• A. $0$
• B. $1$
• C. $2$
• D. $3$
• E. $4$

Answer 1

The correct option is E $4$

Given that:

${\log }_b\left(a\right)=x,{\log }_b\left(c\right)$

$4x+6y=8$

$4{\log }_b\left(a\right)+6{\log }_b\left(c\right)=8$

$\Rightarrow {\log }_b\left(a^4\right)+{\log }_b\left(c^6\right)=8$

$\Rightarrow {\log }_b\left(a^4{c}^6\right)=8$

$\Rightarrow {\log }_b(a^2{c}^3{)}^2=8$

$\Rightarrow 2{\log }_b\left(a^2{c}^3\right)=8$

$\Rightarrow {\log }_b\left(a^2{c}^3\right)=4$

Hence, E is the correct option.