Which expression is equivalent to the glven expression?
4 In 1 + In 3 - In 1

Step-by-step explanation:

Start by observing that ln(1) = 0

So ln 1^4 = 0 as well.

My calculator says that 4 ln(1) + ln (3) - ln1

is ln(3).

I'm not sure it's right.  Is that a bug or is it actually what the answer is? I will accept it is ln3 but I have my doubts -- especially when when there is a zero involved. If you get a different responder to this and something different is said, I would accept that answer.

Very interesting question.

7.3

step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true