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2 years ago

Use the power property to rewrite log3x9.

Mathematics

2 answers:

Kitty [74]2 years ago

9 0

Answer:

$\log _3\left(x^9\right)=9\log _3\left(x\right)$

Step-by-step explanation:

Given the expression

$\log _3\:x^9$

now rewriting the expression

$\log _3\:x^9$

$\mathrm{Apply\:log\:rule\:}\log _a\left(x^b\right)=b\cdot \log _a\left(x\right),\:\quad \mathrm{\:assuming\:}x\:\ge \:0$

$=9\log _3\left(x\right)$

Therefore,

$\log _3\left(x^9\right)=9\log _3\left(x\right)$

dexar [7]2 years ago

7 0

Answer:

Step-by-step explanation:

edge

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A small garden measures 9 ft by 13 ft. A uniform border around the garden increases the total area to 192 ft square. What is the

victus00 [196]

The width of border is 1.5 feet

<h3><u>Solution:</u></h3>

Given that small garden measures 9 ft by 13 ft

A uniform border around the garden increases the total area to 192 ft square

To find: width of border

Let the width of border be "x"

Then the new measures of garden are (9 + 2x) feet and (13 + 2x) feet

The total area of garden = 192 square feet

$(9 + 2x)(13 + 2x) =192$

$117 + 18x + 26x + 4x^2 = 192\\\\4x^2 + 44x - 75 = 0$

<em><u>Let us solve the above equation by quadratic formula</u></em>

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Using the above formula,

For $4x^2 + 44x - 75 = 0$ , we have a = 4 ; b = 44 ; c = -75

Substituting the values of a = 4 ; b = 44 ; c = -75 in above quadratic formula we get,

$\begin{aligned}&x=\frac{-44 \pm \sqrt{44^{2}-4(4)(-75)}}{2 \times 4}\\\\&x=\frac{-44 \pm \sqrt{1936-1200}}{8}\\\\&x=\frac{-44 \pm \sqrt{3136}}{8}\\\\&x=\frac{-44 \pm 56}{8}\end{aligned}$

$\begin{aligned}&x=\frac{-44+56}{8} \text { or } x=\frac{-44-56}{8}\\\\&x=\frac{12}{8} \text { or } x=\frac{-100}{8}\\\\&x=1.5 \text { or } x=-12.5\end{aligned}$

Since "x" cannot be negative,

we get x = 1.5

Thus width of border is 1.5 feet

4 0

3 years ago

A door with width 4.20m has an arc as shown in the diagram. Find: a) the radius of the arc, to the nearest cm. b) the length of

Ksju [112]

Hi there!

$R = \frac{2.1}{sin 67.5}$

$Arc = R$ $\frac{3\pi }{4}$

(A)

Hope this helped you!

5 0

2 years ago

Read 2 more answers

A room in the shape of a triangle has sides of length 7 yd, 8 yd, and 11 yd. If carpeting costs $17.50 a square yard and padding

Monica [59]

770 dollars I think I'm not 100% sure

7 0

3 years ago

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¿CUAL ES EL PERIMETRO DE UN RECTANGULO SABIENDO QUE SU ANCHO ES 3/4 DEL LARGO Y BEL LARGO MIDE 2,55M?

m_a_m_a [10]

Answer:

Perímetro = 8.925 metros

Step-by-step explanation:

La formula del perímetro de un rectángulo es:

perímetro = 2(ancho + largo)

en este caso:

p = 2(a+b)

a = 3b/4

b = 2.55m

a = ancho del rectángulo

b = largo del rectángulo

entonces:

sustituyendo el valor de la segunda ecuación

p = 2((3b/4)+b)

p = 2((3b/4)+(4b/4))

p = 2(7b/4)

p = 14b/4

p = 7b/2

p = 7*2.55/2

p = 8.925m

3 0

3 years ago

Consider this cube with a volume of 64 cubic centimeters.

Eduardwww [97]

Answer:

This is a perfect cube.

The side length is 4.

Taking the cube root of the volume will determine the side length.

Step-by-step explanation:

We are told that:

A cube has volume 64 centimeters cubed.

The formula for the volume of a cube = s³

Where s = side length

Hence

64 cm³ = s³

We can find s by finding the cube root of both sides

Hence,

cube root(64) = cube root(s³)

s = 4 cm

Note that 64 is a perfect cube because 4 × 4 × 4 = 4³ = 64 cm³

Therefore, it can be concluded of the cube that:

This is a perfect cube.

The side length is 4.

Taking the cube root of the volume will determine the side length.

3 0

2 years ago