Question

Solve the exponential equation. Express the solu 5⁴ˣ⁺¹=6ˣ⁺²

Answer 1

`{5}^(4x +1 ) = {6}^(x + 2)`

`ln( {5}^(4x + 1) ) = ln( {6}^(x + 2) )`

(4x + 1)(ln 5) = (x + 2)(ln 6)

4x ln 5 + ln 5 = x ln 6 + 2 ln 6

4x ln 5 - x ln 6 = 2 ln 6 - ln 5

x(4 ln 5 - ln 6) = 2 ln 6 - ln 5

x = (2 ln 6 - ln 5)/(4 ln 5 - ln 6)