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Misha Larkins [42]

3 years ago

8

2logx-log(x-1)=log(x-2)

1 answer:

Nata [24]3 years ago

8 0

2 log(<em>x</em>) - log(<em>x</em> - 1) = log(<em>x</em> - 2)

log(<em>x</em>²) - log(<em>x</em> - 1) = log(<em>x</em> - 2)

log(<em>x</em>² / (<em>x</em> - 1)) = log(<em>x</em> - 2)

<em>x</em>² / (<em>x</em> - 1) = <em>x </em>- 2

<em>x</em>² = (<em>x</em> - 1) (<em>x</em> - 2)

<em>x</em>² = <em>x</em>² - 3<em>x</em> + 2

0 = -3<em>x</em> + 2

3<em>x</em> = 2

<em>x</em> = 2/3

But notice that 2/3 - 1 = -1/3 < 0, and log(<em>x</em> - 1) is undefined so there are no real solutions.

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IRINA_888 [86]

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andrew-mc [135]

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Oliga [24]

Let

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y------> the width of the rectangle

we know that

The area of the rectangle is equal to

$A=x*y$

The area of the two congruent right triangles is equal to the area of the rectangle

$A=2*44=88\ in^{2}$

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Substitute equation B in equation A

$x*[x-3]=88$

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Using a graph tool-------> solve the quadratic equation

see the attached figure

The solution is

$x=11\ in$ -----> the length of the rectangle

Find the value of y

$88=11*y$

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Statements

<u>case A)</u> The area of the rectangle is $88$ square inches

The statement is True

See the procedure

<u>Case B)</u> The equation $x*[x-3]=44$ can be used to solve for the dimensions of the triangle

The statement is False

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<u>case C)</u> The equation $x^{2} -3x-88=0$ can be used to solve for the length of the rectangle

The statement is True

see the procedure

<u>case D)</u>The triangle has a base of $11$ inches and a height of $8$ inches

The statement is True

Because, the base of the triangle is equal to the length of the rectangle and the height of the triangle is equal to the width of the rectangle

<u>case E)</u> The rectangle has a width of $4$ inches

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PtichkaEL [24]

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