Question 763448
Given:
(1) {{{4^(2x-1) = 5^(x+2)}}}
Take the LOG of each side to get
(2) {{{(2x-1)*LOG(4) = (x+2)*LOG(5)}}} or
(3) {{{2*LOG(4)*x - LOG(4) = LOG(5)*x + 2*LOG(5)}}} or
(4) {{{2*LOG(4)*x - LOG(5)*x = LOG(4) + 2*LOG(5)}}} or
(5) {{{(LOG(4^2)-LOG(5))*x = LOG(4)+LOG(5^2)}}} or
(6) {{{(LOG(16)-LOG(5))*x = LOG(4)+LOG(25)}}} or
(7) {{{LOG(16/5)*x = LOG(4*25)}}} or
(8) {{{LOG(3.2)*x = LOG(100)}}} or
(9) {{{x = LOG(100)/LOG(3.2)}}} or
(10){{{x = 2/0.50515...}}} or 
(11) {{{x = 3.959}}}
To check put x of (11) into (1) and you will get
(12) 14638 = 14638
Answer: x = 3.959