Question

Find the value of x in 4000(1.5x) = 25,000. show all work

Answer 1

4000(1.5)x = 25,000
25000/4000 = 1.5x
6.25 = 1.5x
25/6 = x

Answer 2

4000(1.5x)=25000  divide both sides by 4000

1.5x=6.25  divide both sides by 1.5

x=25/6

x=4 1/6

But that is pretty simplistic, I suspect that you actually meant this was an exponential function of the form:

4000(1.5^x)=25000  divide both sides by 4000

1.5^x=6.25  take the natural log of both sides

xln(1.5)=ln(6.25)  divide both sides by ln(1.5)

x=ln(6.25)/ln(1.5)

x≈4.52  (to nearest hundredth)