Question

The value of x for which ${\left(\frac{7}{12}\right)}^{-4}\times {\left(\frac{7}{12}\right)}^{3x}={\left(\frac{7}{12}\right)}^5$ is

(a)-1

(b) 1

(c) 2

(d) 3

Answer 1

${\left(\frac{7}{12}\right)}^{-4}\times {\left(\frac{7}{12}\right)}^{3x}={\left(\frac{7}{12}\right)}^5$

$\Rightarrow {\left(\frac{7}{12}\right)}^{3x-4}={\left(\frac{7}{12}\right)}^5$

$3x-4=5\Rightarrow 3x=5+4=9$

$\Rightarrow x=\frac{9}{3}=3$