Question

Tick (✓) the correct answer
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

(d) 3

$$\begin{gathered} {\left(\frac{7}{12}\right)}^{-4}\times {\left(\frac{7}{12}\right)}^{3x}={\left(\frac{7}{12}\right)}^5 \\ \Rightarrow {\left(\frac{7}{12}\right)}^{-4+3x}={\left(\frac{7}{12}\right)}^5 \\ \Rightarrow 3x-4=5 \\ 3x=9 \\ \mathrm{or}x=\frac{9}{3}=3 \end{gathered}$$