Question

square root (2/5)^x-4=(125/8)^x​

Answer 1

Answer:

(2/5)^-4 =(125/8)^x

1/(2/5)^4= (5^3/2^3)^x            

(5/2)^4=(5/2)^3x

base on both side are same so comparing powers

4=3x

x=4/3

Step-by-step explanation:

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Answer 2

The value of x is equal to 1.

Step-by-step explanation:

We have,

$(\dfrac{2}{5})^{x-4} =(\dfrac{125}{8})^{x}$

To find, the value of x = ?

∴ $(\dfrac{2}{5})^{x-4} =(\dfrac{125}{8})^{x}$

⇒ $(\dfrac{2}{5})^{x-4} =(\dfrac{5^3}{2^3})^{x}$

⇒ $(\dfrac{2}{5})^{x-4} =(\dfrac{5}{2})^{3}^{x}$

⇒ $(\dfrac{2}{5})^{x-4} =(\dfrac{2}{5})^{-3x}$

[ ∵ $(\dfrac{a}{b})^m=(\dfrac{b}{a})^-m$]

⇒ $(\dfrac{2}{5})^{x-4} =(\dfrac{2}{5})^{-3x}$

Equating the powers, we get

x - 4 = - 3x

⇒ x + 3x = 4

⇒ 4x = 4

⇒ x = 1

Hence, the value of x is equal to 1.