Differentiate: (Do not simplify or plug in any numbers); You must use PR or CR where required. (x^3+4x) e(^5x2)​​​​​​​ln(x^2)* e(^3x)

Q: True or False ln1x + 32 - ln12x2 = ln1x + 32ln12x2

A: Given the equation is  ln x + 3 - ln 2x = ln x+3ln 2x To check whether given statement is True or…

Q: tion size after 9 years. ary.

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Q: Solve th equation for x. log2(log3 x) = 4

A: Consider the given: log2log3x=4Using log Rule:logap=n is equivalent to p=an,log2log3x=4…

Q: Jaox+31 =-3 L+X8 -

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Q: Express in terms of logb 2 / logb 3 / logb 5 logb .55555555555555555 =  logb 2.5 = logb 4/9

A: We have to solve the logarithmic

Q: Solve: ln(x + 2) - ln(4x + 3) = ln (1/x).

A: GivenIn(x+2)-In(4x+3) = In(1/x)We have to solve this equation We have In(x+2)-In(4x+3) = In(1/x)We…

Q: Describe Mathematical derivation for graphical assessment of exponential and Weibull Models

A: Here we have to describe Mathematical derivation for graphical assessment of exponential and Weibull…

Q: The value of business, currently priced at 100000 Rial, is expected to increase by 20% a year. After…

A: The exponential growth is defined by the equation, , where r is the growth rate, P0 is the initial…

Q: Show that ln11 + e2x 2 = 2x + ln11 + e-2x2.

A: Here we have to prove that;  ln(1+e2x)= 2x+ln(1+e-2x)

Q: Solve: ln x = ln(x + 6)- ln(x - 4)

A: The properties of logarithms can be used to solve the problem. Now, it is observed that the…

Q: Solve: ln(x - 3) = ln(7x - 23) - ln(x + 1).

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Q: Solve ln(x^2−5x)=ln(6)

A: We have to solve

Q: V1024(V64)*) Express as a single exponent with a base of 2. Show all detailed work including the use…

A: Given:     To determine: Express the given expression as a single exponent of base 2.

Q: 6) In(x²) = (ln x)²

A: These are all unrelated problems since anyone can be solve without any help of another. So by…

Q: Find exponential equation by using these two point (-2,6) and (3,1)

A: Consider y=aebx for some real numbers a and b. As (-2,6) satisfies the equation,…

Q: ln(x+2)=7

A: We have to solve for x

Q: popultaion of a southern city folow exponential law.  if the population doubled in size over 14…

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Q: Without showing the details, explain how to condense ln x - 2 ln(x + 1).

A: Given: lnx-2lnx+1

Q: Expand log6 (64x³[4x+1] ÷ 2x-1)

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Q: x3tanx

A: Given that :   Integrate( x+logx-x3tanx)

Q: Express in terms of sums and differences of logarithms:

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Q: Logx=log12-2log2+log3

A:

Q: Expand. ln(square root of 9x/x-9)

A: It can be expanded using the properties of ln as  ln(AB)c = c {ln(AB)} = c ( lnA + lnB)

Q: 4Log46 - log44-2

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Q: What exponential function will pass through both (2,4) and (5,7)?

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Q: Solve 3 log 80 - ln 5log 5

A: 3log80-ln5log5 Now, simplifying the above expression using the property of logarithms.…

Q: A certain ball is dropped from a height of x feet. It always bounces up to 2/3x feet.  Suppose the…

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Q: Solve ln(3x+2)−ln(10)=ln(5)

A: Given that       ln(3x + 2) - ln(10) = ln(5)

Q: Find the doubling time for a city whose population is growing by 23% per year. pling time is years.

A: To find the doubling time for a city whose population is growing by 23% per year.

Q: Express in terms of sums and differences of logarithms

A: Recall the following facts.

Q: use exponent laws to explain why 3 ln 2 is equivalent to ln8

A: By exponent law     mlna = lnam    for any a and m.

Q: log,(2x+6)-log4lx-1)=1

A:

Q: Simplify and condense 2(ln(x)-ln(x+1)+3/2ln(x-1))

A: 2(ln(x)-ln(x+1)+32ln(x-1))=2lnxx+1+lnx-132

Q: A computer loses 35% of of its value each year. If the computer cost $600 new, calculate its value…

A: A computer loses 35% of of its value each year. If the computer cost $600 new, calculate its value…

Q: Differentiate logx 2

A: We have to find the derivative

Q: solve for x : log6(x-6)+log6(x+6)=log6(5x)

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Q: express ln 3√4 in terms of ln 2 and/or ln 3

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Q: lim log, (8X – 4) x→∞

A: The given limit is: limx→∞log28x-4 This can be written as:…

Q: Express log10 ( 1000x7 / y5 ) as a sum, difference, and/or multiple of logarithms. If possible,…

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Q: Find the total accumulated amoun

A: Given: Invested amount = $6500 Interest rate = 5 %

Q: Gasoline prices are rising at a rate of 0.4​% per month. What is their doubling​ time? By what…

A: The doubling time formula is Doubling time=log(2)log(1+increase) Where increase is the constant…

Q: How long will it take to triple your investment at 6% interest compounded con-tinuously.

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Q: Use the properties of logarithms to expand the expression y8 In x13 z16 in a form with no logarithm…

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Q: Express log,(9AB) in terms of log ,4 and log, Bin simplest form.

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Q: Value of log2 32+ log₂ 16, will be.

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Q: Solve for x 2ln (x-5)= ln (x+7)+ln6

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Q: solve, log(x)+log(x+1)=2 . please show work.

A: using the  formula logm+logn=logmn

Q: 2log46-log49

A: