How do you solve ${(\frac{1}{4})}^{2 x} = {(\frac{1}{2})}^{x}$ $(1/4)^(2x)= (1/2)^x$ ?

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How do you solve ${(\frac{1}{4})}^{2 x} = {(\frac{1}{2})}^{x}$ $(1/4)^(2x)= (1/2)^x$ ?

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Answer 1 · 2018-07-25T18:52:25

$x = 0$ $x=0$

Explanation:

Given that

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

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

${(\frac{1}{2})}^{2 \cdot 2 x} = {(\frac{1}{2})}^{x}$ $(1/2)^{2\cdot 2x}=(1/2)^x$

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

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

$4 x = 2 x$ $4x=2x$

$2 x = 0$ $2x=0$

$x = 0$ $x=0$

Answer 2 · 2018-07-25T19:34:27

$x = 0$ $x=0$

Explanation:

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

$For {(\frac{1}{2})}^{4 x} = {(\frac{1}{2})}^{x} \Rightarrow x = 0$ $"For "(1/2)^(4x)=(1/2)^xrArrx=0$

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How do you solve ${(\frac{1}{4})}^{2 x} = {(\frac{1}{2})}^{x}$ $(1/4)^(2x)= (1/2)^x$ ?

2 Answers

Explanation:

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