What is the root of the equation 7^(-2^x)=4

x = log((2 i π n_1)/log(7) - log(4)/log(7))/log(2) + (2 i π n_2)/log(2) for n_1 element Z and n_2 element Z

Step-by-step explanation:

Solve for x:

7^(-2^x) = 4

Take reciprocals of both sides:

7^(2^x) = 1/4

Take the logarithm base 7 of both sides:

2^x = (2 i π n_1)/log(7) - log(4)/log(7) for n_1 element Z

Take the logarithm base 2 of both sides:

 x = log((2 i π n_1)/log(7) - log(4)/log(7))/log(2) + (2 i π n_2)/log(2) for n_1 element Z and n_2 element Z