Question

Find the value of x for which ${\left(\frac{4}{9}\right)}^4\times {\left(\frac{4}{9}\right)}^{-7}={\left(\frac{4}{9}\right)}^{2x-1}.$

Answer 1

Given:
${\left(\frac{4}{9}\right)}^4\times {\left(\frac{4}{9}\right)}^{-7}={\left(\frac{4}{9}\right)}^{2x-1}$

$\therefore$ ${\left(\frac{4}{9}\right)}^{(4-7)}={\left(\frac{4}{9}\right)}^{-3}={\left(\frac{4}{9}\right)}^{2x-1}$

$$\begin{gathered} \Rightarrow 2x-1=-3 \\ 2x=-3+1=-2 \\ \Rightarrow x=-1 \end{gathered}$$