Solve the equation of (½) log4 (3x - 5) = log4 5.

Hello:

1) 3x-5 > 0 : x > 5/3

(½) log4 (3x - 5) = log4 5.

log (4 (3x - 5)) ^ (½) = log4 5.

log (√4 (3x-5)) = log45

√4 (3x-5) = 45

(√4 (3x-5)) ² = 45²

4 (3x-5) ² = 45²

(3x-5) ² = (45/2) ²

3x-5 = 45/2 or 3x-5 = - 45/2

3x = 5 + 45/2 or 3x = 5 - 45/2

x = 55/6 or x = - 35/6 (refused) because : x > 5/3

conclusion : one solution is : 55/6

The answer is 10 to that equation