Question 1009828
start with:


log(3x-1) - log(2) = 3


since log(a) - log(b) = log(a/b), the equation becomes:


log((3x-1)/2) = 3


this is true if and only if 10^3 = (3x-1)/2


since 10^3 = 1000, then:


1000 = (3x-1)/2


multiply both sides of this equation by 2 to get:


3x-1 = 2000


add 1 to both sides of the equation to get:


3x = 2001


divide both sides of the equation by 3 to get:


x = 667


that's your solution.


when x = 667, log(3x-1) - log(2) = 3 becomes log(3*667-1) - log(2) = 3 which becomes 3 = 3.


this confirms the solution is correct.


your solution is that x = 667.