4^x = 8x
Rewrite 4^x as 2^(2x) and 8 as 2^3
2^(2x) = 8x
2^(2x) = 2^3 * x
Solve algebraically
This equation is transcendental, so exact algebraic solution is difficult. We can try substitution or numerical approach.
Test small integer values
x = 1: 4^1 = 4, 8*1 = 8 not equal
x = 2: 4^2 = 16, 8*2 = 16 works
x = 0: 4^0 = 1, 8*0 = 0 no
x = -1: 4^(-1) = 1/4, 8*(-1) = -8 no
Conclusion
The solution is:
x = 2