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

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)

4000 (1.5) x = 25,000

25000/4000 = 1.5x

6.25 = 1.5x

25/6 = x