103 Rer the logarithm log232 in terms of the common logarith

103 Rer the logarithm log,232 in terms of the common logarithm (base 1o) 0 D) log 4232 B) log 232 log 232)/ (log 4) A) (log 4) (log 232) Condense the expression 3(logx -logy) to the logarithm of a single term. A)x log B) log D) 3(logx-logy E) log 19. (5 peins) Find the exact value of Ine to - In ve without using a calculator. SHOW YOUR W (S points) An initial investment of S9000 grows at an annual interest rate of 7% compounded continuously. How long will it take to double the investment? logarithms if calculator is not permitted. 20. Leave your answer in term 3/7, is a root of f(x) = 7x3-17x2 + 13x-3, use synthetic divis 21. (5 points) If factor the polynomial completely and list all real solutions of the equation.

Solution

19) ln e^4.50 - ln sqrt e

ln e^4.50 = 4.50

ln sqrt e = 1/2

so now we have

4.5 - 1/2 = 4

20) initial investment = $ 9000

annual interest rate = 7% compounded continuously

time to double the investment

9000*2 = 9000 e^ .07t

dividing both sides by 9000

2 = e^.07t

ln 2 = .07t

so it takes t = ln 2 / 0.07 years to double the investment