Question

2^
${2}^{4x - 1 = {2}^{x} }$
4x-1=2^x

Answer 1

Answer:

x = 1/3

Step-by-step explanation:

The easy way:

4x - 1 = x then 3x = 1 so x = 1/3. If you want another proof:

$2^{4x-1} = 2^x\\\dfrac{2^{4x}}{2} = 2^x \\\dfrac{2^{4x}}{2^x} = 2\\2^{4x -x} = 2 \\2^{3x} = 2 \\log_2 (2^{3x}) = log_2 (2)\\3x log_2(2) = log_2(2) \\x = \dfrac{1}{3}$