Rewrite f(x) as a nested exponential-logarithm expression :
[tex]\left(\ln(3x)\right)^{2x} = \exp\left(\ln\left(\ln(3x)\right)^{2x}\right)[/tex]
(where [tex]\exp(x) = e^x[/tex])
One of the properties of logarithms lets us drop the exponent as a coefficient:
[tex]\exp\left(\ln\left(\ln(3x)\right)^{2x}\right) = \exp\left(2x\ln\left(\ln(3x)\right)\right)[/tex]
Now, by the chain rule, we have
[tex]f(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \implies \\\\ f'(x) = \left(\exp\left(2x\ln\left(\ln(3x)\right)\right)\right)' \\\\ f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left(2x\ln\left(\ln(3x)\right)\right)'[/tex]
By the product rule,
[tex]f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left( (2x)' \ln\left(\ln(3x)\right) + 2x\left(\ln\left(\ln(3x)\right)\right)' \right) \\\\ f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left( 2\ln\left(\ln(3x)\right) + 2x\left(\ln\left(\ln(3x)\right)\right)' \right)[/tex]
By the chain rule again,
[tex]f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left(2\ln\left(\ln(3x)\right) + 2x \cdot \dfrac1{\ln(3x)} \cdot \left(\ln(3x)\right)' \right) \\\\ f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left(2\ln\left(\ln(3x)\right) + \dfrac{2x}{\ln(3x)} \cdot \dfrac1{3x} \cdot (3x)' \right) \\\\ f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left(2\ln\left(\ln(3x)\right) + \dfrac{2}{3\ln(3x)} \cdot 3 \right) \\\\ f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left(2\ln\left(\ln(3x)\right) + \dfrac{2}{\ln(3x)} \right)[/tex]
Then simplify this to
[tex]f'(x) = \boxed{\left(\ln(3x)\right)^{2x} \left(2\ln\left(\ln(3x)\right) + \dfrac{2}{\ln(3x)} \right)}[/tex]
if Austin burns 120 calories per 30 minutes of weight training how many calories would he burn in 10 minutes?
please help I have a test in 1 hour and I need to know this by then!
Answer:
40 calories per 10 min
Step-by-step explanation:
Because 30 divided by 3 is 10 and 120 divided by 3 is 40
a teacher has 7 pack of 12 pencils and 2 packs of 54 pencils.the teacher shares these pencils out into 8 pencil pot.how many pencils with be in each pot?
Answer:
24
Step-by-step explanation:
solve for t: 2-16t=6(-3t+2)
Answer:
t = 5Step-by-step explanation:
Just let me know if you want an explanation and I will do it.
Hope this helped. A brainliest would be very much appreciated. (I need 3 brainliest so I can level up) :)
Will mark BRAINLIEST if correct
Answer:
the answer is 9 square meters
I REALLY NEED HELP PLS.....
Answer:
The last two.
[tex] - 5x + 3 \: and \: - 2x + 3 - 3x[/tex]
Step-by-step explanation:
Simplify the first set of parentheses to get
[tex] - 5 \frac{1}{3} x[/tex]
Simplify the second set of parentheses by distributing the negative. It will change the signs in the parentheses.
[tex] \frac{1}{3} x + 3[/tex]
Add (really subtract since the signs are different) the like terms.
[tex] - 5x + 3[/tex]
Three friends participated in a "Biggest Loser" weight loss competition. The table below shows their starting weight and the weight after two months:
Starting Weight
Weight After Two Months
Jacob
225 pounds
207 pounds
Timothy
200 pounds
188 pounds
Hamza
280 pounds
259 pounds
Who lost the biggest percentage of his starting weight?
You need to find the percentage of weight loss for each participant.
To find the percentage of weight loss use the formula
Starting weight – Weight after two months x 100
Starting Weight
Answer:
Jacob lost the biggest percentage of his starting weight.
Jacob: 8%
Timothy: 6.4%
Hamza: 7.5%
Formula: (initial weight - new weight)/initial weight times 100.
Step-by-step explanation:
Jacob: 225 pounds - 207 pounds = 12 pounds
x/100 = 12/225
= 1800/225
= 8%
Timothy: 200 pounds - 188 pounds = 12 pounds
x/100 = 12/188
= 1200/188
= 6.4%
Hamza: 280 pounds - 259 pounds = 21 pounds
x/100 = 21/280
= 2100/280
= 7.5%
log2 (x - 1) - log6(x + 2) = 2
Answer:
log2(x - 1) - log6(x + 2) = 2
x ≈ 12.1485
If you divide the age of the first President Bush when he was inaugurated by 2 and add 14 years, you get the age of President Clinton when he was first inaugurated. How old was President G.H.W. Bush when he was inaugurated?
Answer:
64Step-by-step explanation:32+14=46
Step-by-step explanation:
lf you divide the age of the first President Bush when he was inaugurated by 2 and add 14 years, you get the age of President Clinton when ...
1 answer
Age of President G.H.W. Bush is 37.
What is Unitary Method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Age of President Bush = 54,
So, Age of President Clinton
=(54/2) + 14
=27+14
=41
Now, Age of President G.H.W. Bush
=46/2+14
=23+14
=37
Hence, the age of President G.H.W. Bush is 37.
Learn more about unitary method here:
https://brainly.com/question/22056199
#SPJ5
In a recent year, 27.4% of all registered doctors were female. If there were 55,600 female registered doctors that year, what was the total number of registered doctors?
Answer:
The total number of registered doctors is 202,920 rounded.
Step-by-step explanation:
Solve for (x) in this equation: 27.4/100 = 55,600/(x)
You will get the following equation: (x)= (100*55,600) / (27.4) which equals 202,919.708 rounded to 202,920
To double check, you can see that 27.4% of the total given (202,920) equals the 55,600.
You need to travel 260 miles. Driving at a constant speed of 70 miles per hour, will it be possible to make this trip in 3 hours?
yes or no (please answer quick please)
Answer: No
Step-by-step explanation
Amelia's garden is 7 feet long and 8 feet wide. What is the area of Amelia's garden?
Answer:
10 feet long each because 8 × .25 is 2 and 8 + 2 is 10
Step-by-step explanation:
Brainliest?
What usually happens to main characters by the end of the story?
A. They fall in love.
B. They are defeated by the antagonist.
C. They grow, change, or learn an important lesson.
D. They find treasure beyond their wildest dreams.
Here's your answer:
C. They grow, change, or learn an important lesson
You get this answer because the MC (Main Character) goes on a journey or adventure to seek something and they will learn new things on their way and grow up from who they used to be.
I hope this helps you out! ^-^
Help Math HW due at 11:59 PM! What is -18=7y+6?
Answer:
y=3.4
Step by-step explanation:
-18=y+6
-6
-24=7y
-24/7=7/7y
y=3.428571
Answer:
y=-4
Step-by-step explanation:
-18=7y+6
-24=7y
y=-24/7(3.428571429)
Venetta buys 2 pounds of pistachios and 3 pounds of almonds. The pistachios cost $4 more per pound than the almonds. She pays a total of $48. Which of the following are true? Select all that apply.
A. One pound of pistachios plus 1 pound of almonds cost $20.
B. The pistachios cost twice as much per pound as the almonds.
C. Reducing the number of pounds of almonds by 1 results in a total cost of $40.
D. The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48.
E. The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.
The options that are true include:
A. One pound of pistachios plus 1 pound of almonds cost $20.
C. Reducing the number of pounds of almonds by 1 results in a total cost of $40.
E. The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.
Cost of almond = a
Cost of pistachios = a + 4
Therefore, based on the information given, the equation to solve the question will be:
2(a + 4) + 3a = 48
Collect like terms
2a + 8 + 3a = 48
5a = 48 - 8
5a = 40
a = 40/5
a = 8
Almonds cost $8
Pistachios cost $12
In conclusion, the correct options are A, C, and E.
Read related link on:
https://brainly.com/question/24429956
Solve for c.
-2c + -6 = 2
C =
Help is highly appreciated thank u
Answer:
c= -4
Step-by-step explanation:
3. A cookie recipe called for 3 1/2 cups of sugar for every 2 1/6 cups of flour.
a. What is the unit rate of cups of
sugar to cups of flour?
b. How many cups of sugar would
you need if you used 6 cups of
flour?
3.5 to 2.167
2.80
Step-by-step explanation:
The ratio of Kelly's money to Vera’s money was 7:3. After Kelly spent $35, she had $9 more than Vera. How much money did each girl have at first?
Change each of the mixed numbers below into a fraction 1 3/8
Answer:
11/8
Step-by-step explanation:
1 3/8 = 1 + 3/8 = 1/1 + 3/8 = 8/8 + 3/8 = 11/8
The diameter of Jupiter is about 1.4 x 10 5 kilometers. The diameter of Mars is snout 6.8 x 10 3 kilometers. About how many times greater is Jupiter’s diameter of Mars
Answer:
Jupiter's diameter is "about" 21 times greater than Mars with an exact answer of around 20.588
Step-by-step explanation:
Jupiter = 1.4 x [tex]10^{5}[/tex] = 140,000
(1.4 "plus 5 places" is how I think of it to make it easier)
Mars = 6.8 x 10³ = 6,800
To find how many times greater Jupiter is than Mars we can divide tje diameter of Jupiter by Mars:
140,000 / 6,800 = 20.588235 etc
I am not sure how far you are rounding, but Jupiter's diameter is "about" 21 times greater than Mars
Tara has 3 dogs and 4 cats.
The dogs have a mean weight of x kg.
The cats have a mean weight of y kg.
Write down an expression, in terms of x and y, for the mean weight of all 7 of Tara's pets.
Please help me I need to pass
Answer:
5 / 8
Step-by-step explanation:
3 / 4 = 0.75
5 / 8 = 0.625
5 / 8 is between 1 and 3 / 4.
Identify the domain and the range of the relation shown in the figure.
Answer:
Domain is the X values, Y is the range Values
Step-by-step explanation:
(0,0) both domain and range is 0
(4,-1) 4 is the domain, -1 is the range
(1,5) 1 is the domain, 5 is the range
(-2,-4) -2 is the domain, -4 is the range
(-5,-1) -5 is the domain, -1 is the range
(-5,3) -5 is the domain, 3 is the range
(sorry if this is not the thing you are looking for but this is what I know)
Answer:
Domain: [tex]4\leq x\leq -5[/tex]
Range: [tex]-1\leq y\leq 3[/tex]
Step-by-step explanation:
In a relation, WE CAN IDENTIFY THE DOMAIN AND RANGE by looking at the points.
https://brainly.com/question/11447256
Fred's family wants to switch cell phone plans. Hot Spot Mobile is offering a one-time discount of $50 for families that use multiple phones with their service. Fred's family uses 5 phones, and the salesperson said the first month's payment, which includes the discount and the regular monthly rate for each phone, will be $62.25. What is the regular monthly rate for each phone?
The regular monthly rate for each phone is $22.45.
What is a monthly rate?The monthly rate refers to the amount of money paid every month due to a service or debt.
How to calculate the monthly rate for these cellphones?The monthly rate can be calculated using the following formula.
$62.25 + $50 (discount) / 5 (number of cellphones)This is because the family will pay a total of $62.25 for the 5 cellphones including the discount for the first month. Let's now solve this problem:
$112.25/5 = $22.45Learn more about money in: https://brainly.com/question/2696748
Simplify the expression to a + bi form:
(8 – i) – (10 – 8i)
Answer:
-2+7i
Step-by-step explanation:
(8-i)-(10-8i)
8-i-10+8i
8-10-i+8i
-2+7i
Answer:-2+7i
Step-by-step explanation:
Use the sequence of operations to answer the question.
1. add 3 to b
2. subtract the result inom 8
3. triple the answer
Answer:
(8-(3+b))3
Step-by-step explanation:
first of all, we have to variables, 3 and b that we are told to add
that is, 3+b
we are now told to subtract the answer from 8
that is 8 minis the answer
= 8- (3+b)
lastly we triple the answer to give
(8-(3+b)3
or
3(8-(3+b)
Translate the sentence into an equation.
Two times the sum of a number and 4 equals 9.
Use the variable y for the unknown number.
Answer:
The equation for this sentence is: 9 = 2(4y)
Answer:
2(y + 4) = 9Step-by-step explanation:
Two times the sum of a number and 4 equals 9:
2(y + 4) = 9Whats the answer to this question? ( Branliest )
Answer:
3+jk+k^6
j=2 & k=6
substituting the values, we have
= 3+2(6)+6^3
= 3+12+216
= 231
Ans=231
Step-by-step explanation:
j=2 and k=6
Now
(6)³+2(6)+3216+12+3216+15231A box with a square base and no top is to be made from a square piece of carboard by cutting 3 in. squares from each corner and folding up the sides. The box is to hold 972 in3. How big a piece of cardboard is needed? Your answer is:__ in. by___ in.
show your work
Answer:
24 in by 24 in
Step-by-step explanation:
Height of the box is 3 in, then
area of base is 972/3 = 324 in.
The side of the box base is [tex]\sqrt{324}[/tex] = 18
The side of the square piece of carboard is 18 + 2 x 3 = 24 in.
Use the formula below to find the 25th term in the geometric sequence.
an= (-3)2^n-1
A. -100,663,296
B. -50,331,648
C. -25,165,824
D. 50,331,648
Answer:
B.
Step-by-step explanation:
To solve, substitute 25 in for x:
[tex]a_{x} = (-3)2^x^-^1[/tex]
[tex]a_{x} = (-3)2^2^5^-^1[/tex]
[tex]a_{x} = (-3)2^2^4[/tex]
[tex]a_{x} = (-3)(16777216)[/tex]
[tex]a_{x} = -50331648[/tex]
Need help on this question
Answer:
m < U = 65°
Step-by-step explanation:
Given that m < PTU° = 115°, and that it is a supplement to < UTV, then we can establish that m < UTV = 65° because their angles must add up to 180°.
From this point forward, we'll name < UTV as < T of △VUT.
Now that we have the measure of < T, we can find out the value of the missing angle, < VUT, through the following equation:
180° = m < V° + m < T° + m < U°
180° = m < 50° + m < 65° + x
180° = m < 115° + x
Subtract m < 115 from both sides to isolate x:
180° - m < 115° = m < 115° - m < 115° + x
65° = x
To verify that we have the correct answer, we'll add up all the measures of the three angles of the triangle to see if it sums up to 180°:
180° = m < V° + m < T° + m < U°
180° = m < 50° + m < 65° + m < 65°
180° = m < 50° + m < 65° + m < 65°
180° = 180° (True statement).
Therefore, the measure of the missing angle, < U = 65°