Question

solve this to become brainest​

Answer 1

Given to find the value of x :-

$\bigg(\dfrac{2}{5} \bigg)^{-6}\times\bigg(\dfrac{5}{2} \bigg)^3= \bigg(\ \dfrac{5}{2} \bigg)^{2x-1}$

SOLUTION :-

As we that from exponent and laws

$\bigg(\dfrac{a}{b} \bigg)^{-n}=\bigg( \dfrac{b}{a} \bigg)^n$

So,

$\bigg(\dfrac{2}{5} \bigg)^{-6} =\bigg(\dfrac{5}{2} \bigg)^6$

$\bigg(\dfrac{5}{2} \bigg)^{6}\times\bigg(\dfrac{5}{2} \bigg)^3= \bigg(\ \dfrac{5}{2} \bigg)^{2x-1}$

As we know that ,

$a^m \times a^n = a^{m+n}$

So,

$\bigg(\dfrac{5}{2} \bigg)^{6+3}=\bigg( \dfrac{5}{2} \bigg)^{2x-1}$

$\bigg(\dfrac{5}{2} \bigg)^{9}=\bigg( \dfrac{5}{2} \bigg)^{2x-1}$

As we know that ,

If bases are equal then powers also should be equal

So,

$2x-1 = 9$

$2x= 9+1$

$2x =10$

$x = \dfrac{10}{2}$

$x=5$

So, the value of x is 5