Question

Select the correct answer. What is the value of x in the equation ln (x + 6) – ln (2x – 1) = 1? A. -0.21 B. 0.74 C. 1.35 D. 1.97

Answer 1

Answer: Correct option is (D) 1.97

Explanation:

According to question,

ln (x + 6) – ln (2x – 1) = 1.....(i)

Now by using log rule

Log(a) – Log(b)= Log(a/b)

Equation (i) becomes

Log((x + 6) / (2x - 1)) = 1

Taking anti log on both sides

((x + 6) / (2x - 1)) = e1

We know that

e1 = 2.72

Therefore,

((x + 6) / (2x - 1)) ≈ 2.72

(x + 6) = 2.72 (2x - 1)

x + 6 = 2.72 (2x) - 2.72 (1)

x + 6 = 5.44x - 2.72

8.72 = 4.44x

By cross multiplication we get,

x = 8.72 / 4.44

x = 1.97

Hence the correct value of x is 1.97

Answer 2

Answer: 6!

Step-by-step explanation: Isolate the variables. In order to do that you have to divide each side by factors that don't contain the variables.