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3 years ago

What are the solutions to log3x + log3(x2 + 2) = 1 + 2log3x?

Mathematics

2 answers:

tangare [24]3 years ago

7 0

Answer:

Option C and D are correct

x = 1

x= 2

Step-by-step explanation:

Use logarithmic rules:

$\log_b b = 1$

$\log_b (mn) = \log_b m+ \log_b n$

$\log_b x^n = n\log_b x$

As per the statement:

Given the equation:

$\log_3 x+ \log_3 (x^2+2) = 1+2\log_3 x$

Apply the logarithmic rules:'

$\log_3 x(x^2+2) = \log_3 3 + \log_3 x^2$

Again apply logarithmic rule:

$\log_3 x(x^2+2) =\log_3 3x^2$

then;

$x(x^2+2) = 3x^2$

Divide both sides by x we have;

$x^2+2 = 3x$

Subtract 3x from both sides we have;

$x^2-3x+2=0$

⇒ $x^2-2x-x+2=0$

⇒ $x(x-2)-1(x-2)=0$

⇒ $(x-2)(x-1)=0$

By zero product property we have;

x-2 = 0 and x-1 = 0

⇒x = 2 and x = 1

Therefore, the solution for the given equation are: 1 and 2

PIT_PIT [208]3 years ago

4 0

X=1 & x=2 is the answer i dont know how to explain it but i got it right.

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3 years ago

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An airplane leaves an airport and flies due west 150 miles and then 170 miles in the direction S 49.17°W. How far is the plane f

Ganezh [65]

Answer:

299.99 miles

Step-by-step explanation:

Since the plane traveled due west,

The total angle is 49.17 + 90

Represent that with θ

θ = 49.17 + 90

θ = 139.17.

Represent the sides as

A = 170

B = 150

C = unknown

Since, θ is opposite side C, side C can be calculated using cosine formula as;

C² = A² + B² - 2ABCosθ

Substitute values for A, B and θ

C² = 150² + 170² - 2 * 150 * 170 * Cos 139.17

C² = 22500 + 28900 - 51000 * Cos 139.17

C² = 51400 - 51000 (−0.7567)

C² = 51400 + 38,591.7

C² = 89,991.7

Take Square Root of both sides

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3 years ago

R (-3,1) and S (-1,3) are points on a circle. If RS is a diameter, find the equation of the circle.

ELEN [110]

Answer:

$\sf (x+2)^2+(y-2)^2=2$

Step-by-step explanation:

If RS is the diameter of the circle, then the midpoint of RS will be the center of the circle.

$\sf midpoint=\left(\dfrac{x_s-x_r}{2}+x_r,\dfrac{y_s-y_r}{2}+y_r \right)$

$\sf =\left(\dfrac{-1-(-3)}{2}+(-3),\dfrac{3-1}{2}+1 \right)$

$\sf =(-2, 2)$

Equation of a circle: $\sf (x-h)^2+(y-k)^2=r^2$

(where (h, k) is the center and r is the radius)

Substituting found center (-2, 2) into the equation of a circle:

$\sf \implies (x-(-2))^2+(y-2)^2=r^2$

$\sf \implies (x+2)^2+(y-2)^2=r^2$

To find $\sf r^2$ , simply substitute one of the points into the equation and solve:

$\sf \implies (-3+2)^2+(1-2)^2=r^2$

$\sf \implies 1+1=r^2$

$\sf \implies r^2=2$

Therefore, the equation of the circle is:

$\sf (x+2)^2+(y-2)^2=2$

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2 years ago

Daniel watches one hour of television for every three hours of homework he does each week. If you did 15 hours of homework last

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3 years ago

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A quadrilateral has vertices A, B, C, and D. A line of reflection is drawn so that A is 6 units away from the line, B is 4 units

Kryger [21]

Answer:

The correct option is O B'

Step-by-step explanation:

We have a quadrilateral with vertices A, B, C and D. A line of reflection is drawn so that A is 6 units away from the line, B is 4 units away from the line, C is 7 units away from the line and D is 9 units away from the line.

Now we perform the reflection and we obtain a new quadrilateral A'B'C'D'.

In order to apply the reflection to the original quadrilateral ABCD, we perform the reflection to all of its points, particularly to its vertices.

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I will attach a drawing with an example.

Finally, we only have to look at the vertices and its original distances to answer the question.

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