Question

Find the value of x , if
$(\frac{5}{7}{)}^6(\frac{7}{5}{)}^{-9}=(\frac{5}{7}{)}^{3x}$

Answer 1

Given

${\left(\frac{5}{7}\right)}^6.{\left(\frac{7}{5}\right)}^{-9}={\left(\frac{5}{7}\right)}^{3x}$

${\Rightarrow \left(\frac{5}{7}\right)}^6\times {\left(\frac{5}{7}\right)}^9={\left(\frac{5}{7}\right)}^{3x}$

${\Rightarrow \left(\frac{5}{7}\right)}^{6+9}={\left(\frac{5}{7}\right)}^{3x}$ ---since base is same, powers add up

${\Rightarrow \left(\frac{5}{7}\right)}^{15}={\left(\frac{5}{7}\right)}^{3x}$

$\Rightarrow 15=3x$ ---since base is same, we can compare powers

$\therefore x=5$