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Question

Solve 

1. 6x²-19 -20 =0

 

2. 1/3x = 12 

 

3. 8x-4+3 (x+7) = 6x-3(x-3) 

 

Evaluate 

4. 8^5/3 

 

5.  log₃81 

Answer 1

1)6x² - 19 - 20 = 0 -> 6x² -(19 + 20) = 0 -> 6x² - 39 = 0 

 

divide both sides by 6. x² -13/2 = 0 ->

to factor the expression remember x² - y² = (x + y)(x - y) :  (x - √(13/2))(x + √(13/2)) = 0

 

x = +-√(13/2)

 

2)1/3x = 12 -> multiply both sides by 3x -> 36x = 1 -> x = 1/36.

 

3)8x-4+3 (x+7) = 6x-3(x-3)

   use distributive property

8x - 4 + 3x + 21 = 6x - 3x + 9

 

Group the constants together and x's together on both sides.

 

(8x + 3x) + (21 - 4) = (6x - 3x) + 9

 

11x + 17 = 3x + 9, solve for x.

 

4)8^(5/3) =the cube root of 8 is 2. 2 * 2 * 2 = 8 thus the answer is 2^5 = 32.

 

5)This is asking 3 raised to what exponent will get 81. It the exponent is a whole number we can find this by dividing 81 by 3 and counting how long it takes to get to 1. 

 

81/3 = 27; 27/3 = 9; 9/3 = 3; 3/3 = 1. Four times therefore 3^4 = 81. 

 

 

Answer 2

I will give your hints for each type of question.

 

 

1)

 

You can factoring the left side of the equation using FOIL.  If this doesn't work, use the quadratic formula.

 

 

2)

 

Multiply both sides of the equation by the reciprocal of the coefficient of x.

 

 

3)

 

First, you need to distribute the terms to get rid of the parentheses.  Then move all the x terms to the left side of equation.  Move all the constant terms to the right side of equation.  From there, you can combine like terms on each side.  Then divide both sides of the equation by the coefficient of x.

 

 

4)

 

Turn the rational exponent into the radical terms.

 

³√(8⁵)

 

 

Break up the radical term by its factors.  In other words, apply the rules of radicals.

 

³√(8³) * ³√(8²)

 

 

Notice that one factor has a root and an exponent that cancel each other out.   So you have

 

8 * ³√(8²)

 

 

Then 8² is 64.  And the cube-root of 64 is 4.

 

So your final result is     8*4.   Simplify that.

 

 

 

4)

 

3 raised to what power results in 81?  That exponent is your solution.

Answer 3

1.  collect like terms: 6x² = 39; x² = 13/2; take square root (remember ±) and rationalize denominator.

 

2.  multiply both sides by 3, giving x = 36

 

3.  use distributive property; collect like terms, etc.

 

4.  rewrite as one third of 8⁵ = (2³)⁵ = 2¹⁵ = 32,768.  Note: order of operations requires interpreting what you wrote as "exponentiate 8 to fifth power, then divide whole result by 3"

 

5.  rewrite 81 as 3⁴ and then taking logarithm (b ase 3) is merely grabbing the exponent, so answer is FOUR--because you have BASE AGAREEMENT.  error corrected per note from Michael J.