Help with logarithms ?

I am currently studying logs and am stuck with this question:

Function y=a-2^{bx} intersects y axis at y=4 and x axis at x= 2.58

this makes 4= a-2^{b x 2.58}

Find the constants a and b.

I have no idea on what to do first...

Function intersects y-axis at y = 4 and x-axis at x = 2.58
This does NOT make 4 = a − 2^(b*2.58)
y-intersect and x-intersect are two different points

Function intersects y-axis at y = 4 ----> point (0,4)
4 = a − 2^0 = a − 1
a = 5
y = 5 − 2^(bx)

Function intersects x-axis at x = 2.58 ----> point (2.58, 0)
0 = 5 − 2^(2.58b)
2^(2.58b) = 5
ln(2^(2.58b)) = ln(5)
2.58b ln(2) = ln(5)
b = ln(5) / (2.58 ln(2))
b = 0.89997213

y = 5 − 2^(0.89997213 x)

y = a - 2^(bx)

x = 0, y = 4
4 = a - 2^(b*0)
a = 5

y = 0, x = 2.58
0 = 5 - 2^(b*2.58)
2^(2.58 b) = 5
ln 2^(2.58 b) = ln 5
2.58 b * ln 2 = ln 5
2.58 b = ln 5 / ln 2
b = (ln 5 / ln 2) / 2.58
b ≈ 0.9