How do I solve the following equation

4-7^2x=1

Assuming you mean

4 - 7^(2x) = 1
7^(2x) = 3
Take logarithm to base 7 of both sides
2x log 7 = log 3
x = log 3/(2 log 7)
x = 0.4771/(2 * 0.8451)
x = 0.4771/1.6902
x = 0.2823