Show, by producing a counterexample, that ln(ab) is not equal to (ln a)(ln b).

Q: If y = xtan (a), find y' by using logarithmic differentiation.

A: Important logarithmic property: ln(xn) = n*ln(x)

Q: Suppose $5,000 is invested at 7% intrest compounded continiously. How long will it take the…

A: The investment amount P = $ 5000. The interest rate r = 7% compounded continuously. The final amount…

Q: Determine whether the equation is true or false: ln(5x) + ln 1 = ln(5x). Where possible, show work…

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Q: Explain, in terms of linear approximations, why the  approximation is reasonable. ln 1.05 = 0.05…

A: Given: (1.01)6=1.06

Q: Find the effective rate of interest.; For 4% compounded continuously

A: 4% compounded continuously.

Q: Without using calculator, solve coth−1 x = ln (x + 1).

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Q: Find the time required for an initial investment of $2000 to reach $3500 if the interest is…

A: Topic- continuous compound interest

Q: Find an approximate value of ln20.

A: e3=20.0855369232  We will use this to approximate ln(20)   Let us take a function f(x)=ln(x) And…

Q: Use logarithmic function to find dy/dx, if y=(x^2+5)^sin (2x)

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Q: Find the indicated derivative and simplify. [3x log x³] dx [3x log x³] = dx (Type an exact answer.)

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: How would I calculate the principle value of  ln(-ie)

A: Given, z=lne-i Convert e-i to polar form. For a complex number a+bi  polar form is given by,…

Q: The half-life of Zn-71 is 2.4 minutes. If one had 135.0g at the beginning, how many grams would be…

A: We have to find

Q: At the time of the birth of a child, a parent wants to begin a college fund that will grow to $43000…

A: Given that the interest is compounded continuously

Q: Find the time it takes for $8,900 to double when invested at an annual interest rate of 2%,…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: How long will it take to triple $12000, invested at 4.5% compounded continuously? (A = Pe*t) %3D

A: We are given the initial value to be $12000 and rate r = 4.5% = 0.045. Now, we need to find that how…

Q: How long would it take for a principal ofP to double if invested at 7% compounded continuously?

A: Given, for a principal of P to double if invested at 7% compounded continuously.

Q: $400 invested at 7% compounded continuously after aperiod of 3 years

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Q: How long, to the nearest year, will it take an investment to triple if it is continuously compounded…

A: Formula to calculate continuously compounded interest: A = Pert where, A is Amount at time t,P =…

Q: )=1/x. Using this, compute the

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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: Determine whether the following statement is true or false, and explain why. The derivative of ln kx…

A: if y = ln x Then y'=1x

Q: A CERTAIN RADIOACTIVE MATERIAL IS KNOWN TO DECAY AT A RATE PROPORTIONAL TO THE AMOUNT PRESENT. IF…

A: Given that, after one hour, the 10% of the material is decayed. find the expression of the material…

Q: In the given question/ as follows, solve for x accurate to three decimal places?   ln x = 2

A: We know that, from the property of logarithm lna=b⇔eb=a

Q: Evaluate the derivative. * d (log10 (x)) dx (In(10)) O Option 1

A: we have to find the derivative

Q: What amount must be invested at 9% compounded continuously, so that it will be worth $35,000 after 5…

A: The total amount (A) obtained after t years by investing an initial amount of P in a firm or account…

Q: Find the amount A in dollars of $8000 invested for 30 years at 10% compounded continuously.

A: Given- P= $8000, r=10%, t=30years. To find- The total amount A. Formula used- A=P1+r100n, where A=…

Q: f you invest $10,400 at an interest rate of 2.5% compounded continuously, when will your investment…

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Q: Determine whether the following statement is true or false, and explain why. (ln 3)4 = 4 ln 3

A: We know that, ln an=n ln a ; n is an integer

Q: Approximate the solution to ln 4x = 3.2. Round to 3 decimal places

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Q: The half-life of plutonium-241 is 13 years.  What is the decay constant?  Use the approximation…

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Q: The equation x ln x = 1 has a single solution, Give a short justification for this the claim.

A: Consider the given equation xlnx=1

Q: Find the effective rate of interest for 10% compound continuously.

A: The continuous rate is calculated by raising the number "e" (approximately equal to 2.71828) to the…

Q: How is ln x affected if x is multiplied by et?

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Q: Find dx by logarithnic differentiation. (3x-2)(x"+3)

A: d(logx)/dx = 1/x

Q: How long, to the nearest year, will it take an investment to triple if it is continuously compounded…

A: We can find the required year in the following steps.

Q: Find the derivative of the following exponential and logarithmic functions: (i) ecosx-sinx ii. In(3x…

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Q: How long will it take for an investment to double in value if it earns 62​% compounded​…

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Q: If $3000 is invested at 5% interest, find thẻ välue of the investment at the end of 5 years if the…

A: (As per bartleby guidelines, for multiple questions asked, only the first question will be solved.…

Q: Use logarithmic differentiation to find y′, given y = e2x xx √(x3 + sinh(3x))

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Q: ミr

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Q: How long will it take to double your money if it is invested at a fixed interest rate of 6%…

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Q: Use newton's method to find an approximate solution of ln(x) =3-x. Start with x0 = 10 and find x2.

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Q: Find the first derivative or f(x) of the following functions using the techniques of integration.

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Q: If you invest $5000 compounded continuously at 4% p.a. how much will this investment be worth in 5…

A: The initial amount P=$5000 Rate of interest r=4%=4100=0.04 p.a. The time period t = 5 years

Q: Which of the following functions grow faster than ln x as x→∞?Which grow at the same rate as ln x?…

A: Definition:                                Let f(x) and g(x) be positive for x…

Q: How long does it take an investment to triple at an annual interest rate of 6.45% compounded…

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Q: $3,500 is invested at a rate of 6% coumpounded weekly. What is the amount at the end of 15 years?

A: Principal amount P = $3500 Rate r = 6% weekly             =( 6/52)% annually  Time t = 15 years  =…

Q: Find an equation of the tangent line to the graph of (log æ)cosh(a-10) , x >1 at the point where x =…

A: Given equation is  y=log xcosh (x-10), x>1 at x=10

Q: What is the derivative of : ln cos 3x

A: