What is the exact solution to the equation 2^2x=5^x-1

A ln5/2ln5-ln2

B. ln5/ln5-2ln2

C. ln5/2ln5+ln2

D. - ln5/2ln2+ln5

d option

2ˣ⁺² = 5²ˣ

ln 2ˣ⁺² = ln 5²ˣ apply ln to both sides

(x + 2) ln 2 = 2x ln 5 apply exponent to coefficient log rule

x ln 2 + 2 ln 2 = 2x ln 5 distribute (x + 2) on left side

2 ln 2 = 2x ln 5 - x ln 2 subtract (x ln 2) from both sides

2 ln 2 = x (2 ln 5 - ln 2) factor out (x) from right side

= x divide both sides by (2 ln 5 - ln 2)