Q. If $2^{x}.3^{x + 4} = 7^{x}$, then $x$ is equal to
A) $\frac{4\log_{e}3}{\log_{e}{7 - \log_{e}6}}$
B) $\frac{4\log_{e}3}{\log_{e}{6 - \log_{e}7}}$
C) $\frac{2\log_{e}3}{\log_{e}{7 - \log_{e}6}}$
D) $\frac{3\log_{e}4}{\log_{e}{6 - \log_{e}7}}$
Explanation
(a)
Given, $2^{x}.3^{x + 4} = 7^{x}$
Taking log on both sides, we get
$x\log_{e}{2 + (x + 4)\log_{e}{3 = x\log_{e}7}}$
$\Rightarrow x\left( \log_{e}{2 + \log_{e}3 - \log_{e}7} \right) = - 4\log_{e}3\$
$\Rightarrow x = \frac{4\log_{e}3}{\log_{e}{7 - \log_{e}6}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.