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3 years ago

How to solve x=5 grafting

1 answer:

4 0

So this one is pretty easy actually when x= a number you automatically know it'll be a vertical line cutting through the x axis. So for this problem (x=5) the line will be vertical and cut through the x axis. Hope this helps!

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What is the true solution to the equation below?

Marina CMI [18]

Answer:

The solution is:

$x=4$

Step-by-step explanation:

Considering the expression

$lne^{lnx}+lne^{lnx}^{^2}=2ln8$

$\ln \left(e^{\ln \left(x\right)}\right)+\ln \left(e^{\ln \left(x\right)\cdot \:2}\right)=2\ln \left(8\right)$

$\mathrm{Apply\:log\:rule}:\quad \:log_a\left(a^b\right)=b$

$\ln \left(e^{\ln \left(x\right)}\right)=\ln \left(x\right),\:\space\ln \left(e^{\ln \left(x\right)2}\right)=\ln \left(x\right)2$

$\ln \left(x\right)+\ln \left(x\right)\cdot \:2=2\ln \left(8\right)$

$\mathrm{Add\:similar\:elements:}\:\ln \left(x\right)+2\ln \left(x\right)=3\ln \left(x\right)$

$3\ln \left(x\right)=2\ln \left(8\right)$

$\mathrm{Divide\:both\:sides\:by\:}3$

$\frac{3\ln \left(x\right)}{3}=\frac{2\ln \left(8\right)}{3}$

$\ln \left(x\right)=\frac{2\ln \left(8\right)}{3}.....A$

Solving the right side of the equation A.

$\frac{2\ln \left(8\right)}{3}$

$\ln \left(8\right):\quad 3\ln \left(2\right)$

Because

$\ln \left(8\right)$

$\mathrm{Rewrite\:}8\mathrm{\:in\:power-base\:form:}\quad 8=2^3$

⇒ $\ln \left(2^3\right)$

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

$\ln \left(2^3\right)=3\ln \left(2\right)$

$\frac{2\ln \left(8\right)}{3}=\frac{2\cdot \:3\ln \left(2\right)}{3}$

$\mathrm{Multiply\:the\:numbers:}\:2\cdot \:3=6$

$=\frac{6\ln \left(2\right)}{3}$

$\mathrm{Divide\:the\:numbers:}\:\frac{6}{3}=2$

$=2\ln \left(2\right)$

So, equation A becomes

$\ln \left(x\right)=2\ln \left(2\right)$

$\mathrm{Apply\:log\:rule}:\quad \:a\log _c\left(b\right)=\log _c\left(b^a\right)$

$=\ln \left(2^2\right)$

$=\ln \left(4\right)$

$\ln \left(x\right)=\ln \left(4\right)$

$\mathrm{Apply\:log\:rule:\:\:If}\:\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\:\mathrm{then}\:f\left(x\right)=g\left(x\right)$

$x=4$

Therefore, the solution is

$x=4$

6 0

3 years ago

Read 2 more answers

A sailboat travels a distance of 2 1/2 miles in 1/6 of an hour.Which complex fraction represents the unit rate in miles per hour

Viktor [21]

2 1/2 miles = 1/6 hours
2 1/2 miles * 6 = 1/6 hours * 6
12 1/2 miles = 6/6 hours
12 1/2 miles = 1 hour
12 1/2 miles/hr

8 0

3 years ago

Don ate 160 grams of carbohydrates, 100 grams of fat, and 70 grams of protein today. What is his total calorie consumption for t

Artemon [7]

Answer:

His total calorie consumption for the day is:

Option C. 1.820 kcal

Step-by-step explanation:

Protein and carbohydrates both contain 4 calories per gram, while fat provides 9 calories per gram, then:

1.) 160 grams of carbohydrates contain:

160 grams * (4 cal/gram)=640 cal

2.) 100 grams of fat contain:

100 grams * (9 cal/gram)=900 cal

3.) 70 grams of protein contain:

70 grams * (4 cal/gram)=280 cal

Then, his total calorie consumption for the day is:

T=640 cal + 900 cal +280 cal

T=1,820 cal

T=1,820 cal (1 kcal / 1,000 cal)

T=1.820 kcal

6 0

3 years ago

Find the area of quadrilateral with vertices at points (3,0)(4,5)(-1,4)(-2,-1)

guapka [62]

Answer: 20

Step-by-step explanation:

Let 's complete our quadrilateral to a rectangle ; and subtract from it the area highlighted in red

$\displaystyle \rm S_{\diamond}=6\cdot 5 =30 \\\\ S_{ABCD}=30-(5:2+5:2+5:2+3:2+1\cdot1)=30-(7,5+1,5+1)=\\\\30-10=20 \\\\ S_{ABCD}=20$

4 0

3 years ago

Read 2 more answers

Assume that the government is currently balancing the national budget so that outlays equal tax revenue. Then the economy slips

german

Answer:

The fiscal policy decition will derive in a deficit by at least $50 billion in the country federal budget.

Step-by-step explanation:

Remember that changes in fiscal policy, imply decreases and increases to taxes and government spending.

In a recession situation, everyone would expect an <u>expansionary</u> fiscal policy (two examples would be tax cuts and increased government spending).

6 0

3 years ago