Question 1062603
start with:


log(5) + log(x+2) - log(x-1) = 2


subtract log(5) from both sides to get:


log(x+2) - log(x-1) = 2 - log(5)


since log(2) = 100, this becomes:


log(x+2) - log(x-1) = log(100) - log(5)


this is equivalent to:


log((x+2)/(x-1)) = log(100/5) which is equal to:


log((x+2)/(x-1)) = log(20)


this is true if and only if (x+2)/(x-1) = 20


solve for x to get x = 22/19.


replace x with 22/19 in your original equation and you will see that the equation is true.


you will get log(5) + log(60/19) - log(3/19) = 2


evaluate this using your calculator to get 2 = 2.


this confirms your solution is correct.


your solution is x = 22/19.