Question

what is the solution of (25)^x-2=(125)^2x-4 ? Answer it fastly.

Answer 1

Answer:

$x = \frac{2}{5}$

Step-by-step explanation:

${25})^{x - 2} = ({125})^{2x - 4}$

${(25)}^{x - 2} = {( {(25)}^{2} )}^{2x - 4}$

${25}^{x - 2} = {25}^{2(2x - 4)}$

${25}^{x - 2} = {25}^{4x - 4}$

cancelling 25

$x - 2 = 4x - 4$

$5x = 2$

$x = \frac{2}{5}$

Answer 2

The value of x is equal to 2.

Step-by-step explanation:

We have:

$(25)^{x-2}=(125)^{2x-4}$

To find, the value of x = ?

∴ $(25)^{x-2}=(125)^{2x-4}$

⇒ $(5^2)^{x-2}=(5^3)^{2x-4}$

Using the exponential identity,

$(a^m)^{n}=a^{mn}$

⇒ $(5^)^{2(x-2)}=(5)^{3(2x-4)}$

Equating the power of 5, we get

∴ 2(x - 2) = 3(2x - 4)

⇒ 2x - 4 = 6x - 12

⇒ 6x - 2x = - 4 + 12

⇒ 4x = 8

⇒ x = 2

Thus, the value of x is equal to 2.