Verified answer

log3x + log3(2x-3) = 3

log3(x(2x - 3)) = 3 raise both sides 3^

x(2x - 3) = 27

2x^2 - 3x - 27 = 0

(x + 3)(2x - 9) = 0

x = -3 (impossible to have negative log so no!!!)

or x =9/2 (this is the answer!)

Logs are to base 3 :-

log x + log (2x - 3) = 3

log [ x (2x - 3) ] = 3

x (2x - 3) = 3³

2x² - 3x = 27

2x² - 3x - 27 = 0

(2x - 9)(x + 3) = 0

x = 9/2 , x = - 3

Accept x = 9/2

put the right hand side into log base 3, ie. log3 27

combine left hand side: log3 x + log3 (2x-3), giving u log3 [x(2x-3)]

comparing left side and right side, x(2x-3) = 27

solve for quadratic equation 2x^2 - 3x - 27 = 0 and find x

:)