SOLUTION: (a) (4x+2)(2x) = 32 (b) (3x+2)(9x+3) = 81 (c) log (x-3) + log (x) = 1 (d) log2 (x2 � 6x) = 3 + log2 (1-x)

Question 161945: (a) (4x+2)(2x) = 32
(b) (3x+2)(9x+3) = 81
(c) log (x-3) + log (x) = 1
(d) log2 (x2 � 6x) = 3 + log2 (1-x)

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first two to get you started

1)

Start with the given equation

Distribute

Subtract 32 from both sides

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

or Break up the expression.

or Reduce

So the answers are or

which approximate to or

2)

Start with the given equation

FOIL

Subtract 81 from both sides

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

or Break up the expression.

So the answers are or

which approximate to or
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