Question

1. Use the Laws of Logarithms to combine the expression:

5 log x − 1/3log(x^2 + 1) + 4 log(x − 1)

2. Solve the equation. (Round your answers to four decimal places.) (There should be a smaller and a larger value):

e^2x − 5e^x + 4 = 0

Answer 1

wrong again!!

5 log x − 1/3log(x^2 + 1) + 4 log(x − 1)
= log x^5 - log(x^2 + 1)^(1/3) + log(x-1)^4
= log [x^5(x-1)^4 / (x^2 + 1)^(1/3) ]

2. e^2x − 5e^x + 4 = 0
(e^x)^2 - 5 e^x + 4 = 0
(e^x - 1)(e^x - 4) = 0

e^x = 1, so x = 0
e^x = 4
xlne = ln4
x = ln4

Answer 2

1. 6 log(x − 1) + 4 log(x + 1)
Answer: 2. x = 0.7183, 2.6183