Question

If 125^x = 25/5^x then find for x ​

Answer 1

Answer:

125x=25÷5x 125x × 5x = 25 625x^2=25 [(25^2)]x^2= 25 25 × x^2= 1 x^2=1/25 x=1/5

Answer 2

Given :-

• $125 {}^{x} = \frac{25}{5 {}^{x} }$

To Find :-

• Value of x

Formula to be used :-

$1) \: \: \: a {}^{m} = a {}^{n} \\ \: \: \: \: \: \: \:⟼ m = n \\ \\ 2) \: \: (a {}^{m} ) {}^{n} = a {}^{mn} \\ \\ \\ 3)a {}^{m} \times a {}^{n} = a {}^{m + n}$

Solution :-

$⟼ 125 {}^{x} = \frac{25}{5 {}^{x} } \\ \\ ⟼ 125 {}^{x} \times 5 {}^{x} = 25 \\ \\⟼ (5 {}^{3} ) { }^{x} \times 5 {}^{x} = 5 {}^{2} \\ \\ ⟼ 5 {}^{3x} \times 5 {}^{x} = 5 {}^{2} \\ \\⟼ 5 {}^{4x} = 5 {}^{2} \\ \\ (Comparing \: the \: powers) \\ \\⟼ 4x = 2 \\ \\ ⟼ x = \frac{2}{4} = \frac{1}{2} \: \: \: \: \: \: \: \:$

Hence, value of x is = ½