Question

If 125^x=25/5^x find x

Answer 1

${125}^{x} = \frac{25}{ {5}^{x} } \\ {5}^{3x} \times {5}^{x} = {5}^{2} \\ {5}^{3x + x} = {5}^{2} \\ {5}^{4x} = {5}^{2} \\ if \: bases \: are \: same \: exponents \: are \: also \: equal \\ 4x = 2 \\ x = \frac{1}{2}$

Answer 2

Given:

125^x=25/5^x

To Find:

Find the value of x

Solution:

We need to have basic knowledge of exponential which will be used in the above question. First, we need to make all the terms in terms of 5 to the power something then it will be easy to solve it, so it goes as,

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

Now writing 125 as 3rd power of 5 and 25 as 2nd power of 5

$(5^3)^x=\frac{5^2}{5^x}$

now multiplying the power to the power with each other

$5^{3x}=\frac{5^2}{5^x}$

Now cross multiplying both sides

$5^{3x}*5^x=5^2\\5^{3x+x}=5^2\\5^{4x}=5^2$

Now equating the powers with each other as the base is equal

$4x=2\\x=\frac{1}{2}$

Hence, the value of x is 1/2.