Unit 2B Review

Let x and y be positive constants. Which of the following is equivalent to 5logx+6logy?

• log(x⁵+y⁶)

• log(x⁵y⁶)

• log(x⁵-y⁶)

• log(5x+6y)

Let x and y be positive constants. Which of the following is NOT equivalent to:

log₃(x+3)+2log₃(x-1)-log₃(x+2)

If log3=x and log4=y, which of the following expresses log√12

• ½(x-y)

• ½(xy)

• ½x+2

• ½(x+y)

Approximate log_b18, given log_b2≈0.4307 and log_b3≈0.6827

• 0.8968

• 1.1134

• 1.5441

• 1.7961

Consider the functions f and g given by f(x)=ln(x+8) and g(x)=ln(x-2)+ln(x+8). In the xy-plane, what are all the x-coordinates of the point of intersection of the graphs of f and g?

• x=8

• x=3

• x=8 and x=-3

• x=2 and x=-8

Solve the equation log_ba+log_b5=c for a.

What are all values of x for which ln(x⁵)=ln(x³)+16?

• x=e⁸ and x=-e⁸

• x=-e⁸

• x=e⁸

• x=8 and x=-8

When considering the equation log(x-3)+log(5)>log(x+9), which of the following domains is our initial restriction?

• (3,∞)

• (5,∞)

• (-9,∞)

• (6,∞)

When considering the equation log(x-3)+log(5)>log(x+9), which of the following represents the domain of all solutions to the inequality?

• (3,∞)

• (5,∞)

• (-9,∞)

• (6,∞)

Express y as a function of x. A, B, and C are constant, positive numbers.

log(y-A)=Bx-logC