# How do you solve (1/4)^(2x)= (1/2)^x?

$x = 0$

#### Explanation:

Given that

${\left(\frac{1}{4}\right)}^{2 x} = {\left(\frac{1}{2}\right)}^{x}$

${\left(\frac{1}{2} ^ 2\right)}^{2 x} = {\left(\frac{1}{2}\right)}^{x}$

${\left(\frac{1}{2}\right)}^{2 \setminus \cdot 2 x} = {\left(\frac{1}{2}\right)}^{x}$

${\left(\frac{1}{2}\right)}^{4 x} = {\left(\frac{1}{2}\right)}^{x}$

Comparing the powers of base $\frac{1}{2}$ on both the sides we get

$4 x = 2 x$

$2 x = 0$

$x = 0$

Jul 25, 2018

$x = 0$

#### Explanation:

${\left(\frac{1}{4}\right)}^{2 x} = {\left({\left(\frac{1}{2}\right)}^{2}\right)}^{2 x} = {\left(\frac{1}{2}\right)}^{4 x}$

$\text{For } {\left(\frac{1}{2}\right)}^{4 x} = {\left(\frac{1}{2}\right)}^{x} \Rightarrow x = 0$