Solves a systems of linear equations in two variables.

Which expression is equivalent to log Subscript w Baseline StartFraction (x squared minus 6) Superscript 4 Baseline Over RootInd

lora16 [44]

The logarithmic expression $\rm log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2-8}}$ can be expressed as $\rm 4log_w{(x^2-6)} - {\dfrac{1}{3}}log_w(x^2-8)$ .

Given to us

$\rm log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2-8}}$

<h3>Which expression is equivalent to $\rm log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2-8}}$ ?</h3>

To solve the problem we will use the basic logarithmic properties,

$\rm log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2-8}}$

Using the logarithmic property $\rm log_a\dfrac{x}{y} = log_ax-log_ay$ ,

$=\rm log_w{(x^2-6)^4} - log_w{\sqrt[3]{x^2-8}}$

Using the exponential property $\sqrt[m]{a^n} = a^{\frac{n}{m}}$ ,

$=\rm log_w{(x^2-6)^4} - log_w(x^2-8)^{\dfrac{1}{3}}$

Using the logarithmic property $\rm log_aB^x = xlog_aB$ ,

$=\rm 4log_w{(x^2-6)} - {\dfrac{1}{3}}log_w(x^2-8)$

Hence, the logarithmic expression $\rm log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2-8}}$ can be expressed as $\rm 4log_w{(x^2-6)} - {\dfrac{1}{3}}log_w(x^2-8)$ .

Learn more about Logarithmic Expression:

brainly.com/question/7302008

5 0

3 years ago

8w-6(w-4)=2(w+9) <br> please help asap

uranmaximum [27]

Answer:

w = -7.04 and 1.705

Step-by-step explanation:

First lets distribute.

We have 8w-6w(w-4), so let's distribute the -6w to w and -4

8w-6w^2+24w = 2(w+9)

Now for the other side we distribute 2 to w and 9

8w-6w^2+24w = 2w +18

Now we combine like terms

6w^2+32w = 2w +18

Carry both 2w and 18 to the other side

6w^2 +30w -18 = 0

Now we can factor the equation, i used the quadratic method which is x= -b+- the square root of b^2-4ac /2a (in this case x would be w)

Plugging that in:

x= -32 +- square root of 32^2 -4(6 * -18) / 2(6)

-32 +- square root of 1024 +1728 / 12

-32 +- square root of 2752 /12

-32 +- 52.46 /12

x = -32 - 52.46/12 and -32 + 52.46/12

x= -84.46/12 and 20.46/12

x= -7.04 and 1.705

so w = -7.04 and 1.705

Sorry this was so complicated, but I hope this helps

6 0

2 years ago

Determine whether the lines are parallel, intersect, or coincide<br> y=1/3x+4 <br> x-3y=-12

adell [148]

The slopes of two lines are equal which means that the lines are parallel.

Further explanation:

The slopes of lines are used to find the relationship between two line.

If two lines are parallel, then their slopes will be equal.
If two lines are perpendicular, the product of slopes of both lines will be -1

The standard form of equation of line is:

$y=mx+b$

The coefficient of x is the slope here.

y=1/3x+4

Let m1 be the slope of first line:

$m_1=\frac{1}{3}$

$x-3y=-12\\-3y=-x-12\\-3y=-1(x+12)\\3y=x+12\\\frac{3y}{3}=\frac{x+12}{3}\\y=\frac{x+12}{3}\\y=\frac{x}{3}+\frac{12}{3}\\y=\frac{1}{3}x+4$

Let m2 be the slope of second line

$m_2=\frac{1}{3}$

We can see that:

$m_1=m_2$

The slopes of two lines are equal which means that the lines are parallel.

Keywords: Parallel Lines, Perpendicular Lines

Learn more about lines at:

#LearnwithBrainly

7 0

4 years ago

Please help with this thank you

PtichkaEL [24]

(5,9) (8,33)

(33-9)/(8-5)= 24/3= 8

y-9= 8(x-5)

y-9= 8x-40

y= 8x-31

3 0

3 years ago

What is 2 1/2 and 6 2/3 in simplest form

sergij07 [2.7K]

2 1/2=5/2 and 6 2/3= 20/3

8 0

4 years ago