My Final Question! 50 points and Brainliest!

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