In(x-24)*(x+100)= In(5^3)
Multiply the parentheses
In(x^2+100x-24x-2400)= In(5^3)
Set the arguments equal
x^2-100x-24x-2400=5^3
Collect like terms, evaluate the power and move the constant to the left
x^2+76x-2525= 0
solve via quadratic equation
x= -76*square root of 76^2-4*2525 divided by 2*1
From that you get
-76+ or -126 divided by 2
The two solutions would be -101 or 25
but, the only answer would be 25 as -101 isn't in the defined range, and would make the statement negative
