You can simply solve it this way: Given: 4⁻ᵐ = m Raise both sides to the power of - 1/m: m⁻¹/ᵐ = 4 This can be rewritten as: m⁻ᵐ = (1/2)⁻¹/² And so, m = ¹/₂
The function f(x)=4^-x - x is 1-1, therefore it has only one root, the obvious one being x=1/2. It would take a mediocre student 2 minutes to solve this.
You can simply solve it this way:
Given:
4⁻ᵐ = m
Raise both sides to the power of - 1/m:
m⁻¹/ᵐ = 4
This can be rewritten as:
m⁻ᵐ = (1/2)⁻¹/²
And so, m = ¹/₂
Thats how I solved it. No need to over complicate it.
hi could you explain how you got to the second step of m^-m =1/2^-1/2
Ridiculous way to solve it. It's solvable in one's head without logarithms.
The function f(x)=4^-x - x is 1-1, therefore it has only one root, the obvious one being x=1/2. It would take a mediocre student 2 minutes to solve this.