2^ {2}^{4x - 1 = {2}^(x) } 4x-1=2^x

Question

2^

`{2}^{4x - 1 = {2}^(x) }`
4x-1=2^x

Answer 1

x = 1/3

Explanation:

The easy way:

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

`2^(4x-1) = 2^x\\(2^(4x))/(2) = 2^x \\(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 = (1)/(3)`