Calculus

QUESTION 1

1. Solve the equation.
   2^{x2 –3}= 64

		{6}
		{3}
		{3, -3}
		{, – }

4 points   
QUESTION 2

1. Solve the equation.
   9^2x∙  27^{(3 – x)} =

		{10}
		{-8}
		{-11}

4 points   
QUESTION 3

1. Solve the equation.
   e^{x – 5} = ^{x + 3}

	{8/5}
	{-17/3}
	{-7/5}
	{-8/3}

4 points   
 
 
 
 
 
 
 
QUESTION 4

1. Solve the equation.
   9 ln 5x =36

		{e4}

4 points   
QUESTION 5

1. Solve the equation.
   ^(16) x+1=(2/4)^x–1

		{3/5}
		{-3/5}
		{-6/5}
		{-3/10}

4 points   
QUESTION 6

1. Solve the equation.
   125^{3x – 2}= 25^5x

{-1/6)
{1/6}
{6}
{-6}

points   
QUESTION 7

1. Solve the equation.
   log₂(3x -2) – log₂(x – 5) = 4

		{3/13}
		{18}
		38/5
		{6}

4 points   
QUESTION 8

1. Solve the equation.
   log₅(x + 1) =1 + log₅(x – 1)

4 points   
QUESTION 9

1. Solve the equation.
   e^{6x –1} = (e⁴)^–x

		{0}

4 points   
QUESTION 10

1. Solve the equation.
   log₃₅(x + 70) =3 – log₃₅x

		{-245}
		{245}
		{-175}
		{175}

4 points   
 
 
 
 
 
 
QUESTION 11

1. Solve the equation.
   5^(9 – 2x)= 3125

		{2}
		{1}
		{3}
		{-2}

4 points   
QUESTION 12

1. Solve the equation.
   e^2x= 7

		{2 ln 7}

4 points   
QUESTION 13

1. Solve the problem.
   f(x) =log₃(x + 1) and g(x) = log₃(x – 1).
   Solve f(x) = What point is on the graph of f?

		{8}, (2, 7)
		{2186}, (2186, 7)
		{2}, (2, 9)
		{8}, (2, 3)

4 points   
QUESTION 14

1. Solve the equation.
   log₄₂(x² – x) = 1

		{1, 42}
		{-6, -7}
		{-6, 7}
		{6, 7}

4 points   
 
 
 
QUESTION 15

1. Solve the equation.
   e^{x + 6} = 8

		{e8 + 6}
		{ln 8 – 6}
		{e48}
		{ln 14}

4 points   
QUESTION 16

1. Solve the equation.
   ln  = 2

		{e4 – 2}
		{e4 + 2}
		{e2 – 2}

4 points   
QUESTION 17

1. Solve the equation.
   log₃(x – 5) +log₃(x – 11) = 3

		{14, 2}
		{15}
		{2}
		{14}

4 points   
QUESTION 18

1. Solve the equation.
   16^{x –3} = 8^3x

4 points   
QUESTION 19

1. Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places.
   ln x +ln (x + 5) = -3

		≈ 2.505
		-5 + ≈ 0.020
		≈ -5.010
		≈ 0.010

4 points   
QUESTION 20

1. Solve the equation.
   125^x= 25

4 points   
QUESTION 21

1. Solve the problem.
   f(x) =log₆(x + 3) and g(x) = log₆(x – 2).
   Solve g(x) = What point is on the graph of g?

		{214}, (214, 3)
		{3}, (3, 218)
		{216}, (216, 3)
		{218}, (218, 3)

4 points   
QUESTION 22

1. Solve the equation.
   (e^x)^x∙ e²⁴ = e^11x

		{8}
		{3, 8}
		{-3, -8}
		{3}

4 points   
QUESTION 23

1. Solve the equation.
   ^{6x + 3} = 9^{x– 4}

4 points   
QUESTION 24

1. Solve the equation.
   3 +8 ln x = 10

		{e 7/8}

4 points   
QUESTION 25

1. Solve the equation.
   2 +log₃(2x + 5) – log₃ x = 4

4 points   
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