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:

Answer: 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