Question

o valor de x que satisfaz a igualdade??

Answer 1

√(3/5)^(1-7x) = 25/9 

(3/5)^(1-7x) = (25/9)² 

(3/5)^(1-7x) = 625/81 

(3/5)^(1-7x) = 5^4/3^4 

(3/5)^(1-7x) = (5/3)^4 

(3/5)^(1-7x) = (3/5)^-4 


1 - 7x = - 4 

1 + 4 = 7x 

7x = 5 

x = 5/7                                                  ok   

Answer 2

$\sqrt{ (\frac{3}{5})^{1-7x} }= \frac{25}{9} \\ \\ ( (\frac{3}{5})^ \frac{1}{2} )^{1-7x}= (\frac{5}{3})^2 \\ \\ ( \frac{3}{5} )^{ \frac{1}{2}- \frac{7x}{2} }= ( \frac{3}{5} )^{-2} \\ \\ \frac{1}{2} - \frac{7x}{2} = - 2 \\ \\ 1 - 7 x = - 4 \\ \\ 5=7x \\ \\ x = \frac{5}{7}$