Question

125^x = 25/5^x find the value of X

Answer 1

Answer:

The value of $x$ is $\dfrac{1}{2}$

Step-by-step explanation:

Given that,

$125^{x}=\dfrac{25}{5^{x} }$

Then

$125^{x}\times 5^{x}=25$

We know that

$25=5^{2}\\125 =5^{3}$

Also

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

Using the above facts, we can rewrite the equation $125^{x}\times 5^{x}=25$ as follows.

$(5^{3})^{x}\times 5^{x} = 5^{2}\\\\\implies 5^{3x}\times 5^{x} =5^{2}\\\implies 5^{3x+x}=5^{2}\\\implies 5^{4x}=5^{2}$

On comparing the powers of 5, we get

$4x= 2\\\implies x=\dfrac{2}{4} =\dfrac{1}{2}$