Show that log,(n) € O(log,(n)) for any b>0 with b 1· Generalize this result.

Q: If w=log(ysinx+xsiny) then prove that wxy=wyx

A: If w=log(ysinx+xsiny) then prove that wxy=wyx

Q: 9. What is the maximum value of |Log z| |2| 1? on

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Q: Prove that all exponential functions are not of the same growth order up to big theta (when a and b…

A: Plot the two exponential functions f(x) and g(x) for a > b.

Q: Find a number E such that log (5z + 1) = 2

A: The solution is given below.

Q: The logarithmic expressi on In can be rewritten as (1) 3ln y- 2 In y- 6 (3) 2 1-6 In y (2) 2 (4) Vin…

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Q: log5 6 is irrational

A: We can prove given result by contradiction method:

Q: The simplified form of In(÷-) using logarithmic rule is yz 4ln x+ In y- In z 4 In x- In y-In z 4ln…

A: The objective is to simplify the given expression using logarithmic rule. The given expression is

Q: The effect on the graph of y = log,z if it is transformed to y = log,(z+3)? may be described as Oa…

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Q: If X~U(0,1) then Y=-In{1-X)~ Exponential (^) Pleose Show

A: When two random variables are connected by a bijective mapping and the probability density function…

Q: 105. If f(x) = log, x, show that -f(x) = log1/a X.

A: Given: fx=logax . To show that -fx=log1ax Solution: Property of logarithm states that:…

Q: Suppose a new screening tool is developed for prostate cancer in men with much higher sensitivity…

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Q: 101. Show that log,(x + V – 1) + log.(x - Vr - 1) = 0.

A: To show: loga(x+x2-1)+loga(x-x2-1)=0 Solution: loga(x+x2-1)+loga(x-x2-1)=0 Considering, Left Hand…

Q: 1. Show that (a) Log(-ei) = 1 - ži;

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Q: The union of left ray topo log y and right ray top log y on real numbers is usual topo log y True…

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Q: 4 Evaluate (logyx)'., having given, 1 1 y = log1,x + ; log,0x + log10x + . 00 1+3+5+ ..+ (2y - 1) 20…

A: We have to solve given problem:

Q: Hiw/ prove That: logit 210gi @ log (iti)= 2 log (iti) ® log é#2log Z it z=

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Q: PROVE that log5 100 = 2(1 + log5 2)

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Q: If H(x) = logb 1/x, show that H(b-1/z)= 1/z

A: H(x)=logb1x, we have to show that Hb-1z=1z

Q: Suppose that a and y are real numbers such that log2 (x) = – 3 and log2 (y) 6. Calculate the…

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Q: 4. The domain of the logarithmic function f(x) = log, x is

A: fx=logax

Q: Prove that | log,x| E O(log2 x )

A: It is obvious that log2x≤log2x so, log2x∈Olog2x.

Q: Can you show and explain properteis of the lognormal function: E(e^x) and Var(e^x)

A: Let us say X follow a normal distribution with probability distribution as shown…

Q: The value of c which satisfy the conclusion of Rolle's Theorem for f(x)=log(x²+1)-log(2) on [-1,1]…

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Q: dx Evaluate log - 1+ax 1-ах

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Q: Evaluate loge 7 by Simpson's (i) rd, and (ii) th rules.

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Q: Prove that log(x + y) = log(x) + log(y) if, and only if, y = 1, where x > 1.

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Q: Expand the logarithm fully using the properties of logs. Express the final answer in terms of log x,…

A: log (a.b) = log (a) + log (b) log (an)= n.log(a)

Q: - If y=a² 1-log.x and z=a* 1-log, y , then x is equal to

A: Introduction :

Q: 4. The expression log(sinx) – log(cos.x) , 0<x<, is equal to A. log(sin x cos x)

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Q: 7. Use properties of logarithm to expand In (y³z²Vx – 1)

A: Property of logarithm

Q: 6) Given that x = log, b. write down an %3D expression for b in terms of a and x. log, t that log, t…

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Q: 4- If X is an exponential with parameter 1, then 2X is chi-square with 2 degrees of freedom. O True…

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Q: Evaluate y for the fx)= 4"-5 log,(x) 4*ln 4- Inx 4- x In 9 4- In 9 4'ln 4- x In 9

A: Answer

Q: п/4 Show that log(1+ tan8)d = log2. 8

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Q: (b) Show that 1 1+ 2 tanh- (2) = ; log

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Q: 2 log(x+y) = 3log3 +logx + logy

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Q: 6) If u = log (x² + y²), then prove that log (x² CSScanned with CamScanner dydx ôxôy

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Q: d Find (2"). Type In(x) for the natural logartihtm dx function.

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Q: Prove that| log,x E O(log2 x)

A: We know the relation |_log2x_|≤log2x≤ log2x. That is the floor value of any real number is less than…

Q: 12) eiven AMUEÍVRTAMA, S C«) X22x<0 2x+1, 0<xL2 a) Evaluate f at x = -1,0, and 5. If not defined,…

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Q: Prove the following equation(with appropiate restrictions on the variables) logx–2=log(x/e²)

A: Here we will use the following formulas logab = log a -log blog(ax) = x log alog e = 1 Consider…

Q: Let X-N(0,1); show that X member in exponential family.

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Q: Evaluate So ·∙log 1+ax 1-ax (: ( dx x√√1-x²

A: A very good problem. This problem illustrates the power of differentiating under the integral sign.…

Q: Evaluate / x. sec² 2x. dx. x.tan2x + + ilog(sec2x) + C 2 O log(sec2x) + C O None xan - log(sec2x) +…

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Q: log,(x – 5) + log,(x + 3) = 1 In(5x) + In x = In(100) In x + In(x – 1) = 10 In(x + 25) – In(x – 1) =…

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Q: (a) Prove that log₁ x= -log₁ x where a > 1. a

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