Find the value of x in 4000(1.5^x) = 25,000. Show your work.

Solution:

Given the expression below let us solve for x:

4000(1.5^x) = 25,000

(1.5^x) = 25000/4000

(1.5^x) = 25/4

(15/10)^x = 25/4

(3/2)^x = 5²/2²

(3/2)^x = (5/2)²

Taking log on both sides we have:

log(3/2)^x = log(5/2)²

xlog(3/2) = 2 log(5/2)

x = 2 log(2.5)/log(1.5)

x = 2 [0.9163/0.4055]

x = 2 × 2.2599 = 4.5198

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Find the value of x in 4000(1.5^x) = 25,000. Show your work.

Summary:

The value of x in 4000(1.5^x) = 25,000 is 4.5198