Please help if you can. Thank you

Step-by-step explanation:

x-4 = log (base3) of 6; add 4 to both sides

x= [log (base3) of (2*3) ] +4; split 6 to 2*3

x= [log (base 3) of 3 + log ( base 3) of 2] + 4; use rule log(ab) = log a+log b

x= log (base 3) of 2 + 1+ 4; use rule log (base a) of a = 1

x= log (base 3) of 2 + 5; put in the calculator

x≈5.63

step-by-step explanation:

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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