Use the properties of logarithms to write the expressions in Exercises 43 and 44 as a single term. (sin 0 43. a. Insin 0 – In 5 b. In (3x² – 9x) + In Зx In (4r*) – Inb c. 44. a. Insec 0 + In cos 0 c. 3 lnVr² – 1 – In(t + 1) b. In(8x + 4) – 2 lnc

Q: sun(log(1+z)) 230Log(1+ Suin2) um 2-)0 log(i+sinx)

A: We will use the result  If limx→af(x)g(x) = 00 , then limx→af(x)g(x) = limx→af'(x)g'(x)

Q: .Expand log (1 + sin x) in powers of z as far as the term in r.

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Q: Use the properties of logarithms to write the expressions in as a single term. ln sec θ + ln cos θ

A: Given                 ln secθ + ln cosθ  So,    as           ln x + ln y =ln xy

Q: 10. Let log x 4, log y 5, log z 3. Using properties of logarithm, find the value of %3D log Show…

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Q: 3

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Q: Show that S log(sin x) dx = -log 2.

A: To show that ∫01logsinπxdx=-log2 using the given figure.

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: Use properties of logarithms to expand the logarithmic expressi +2 In (x+2) X VX+2 In %3D (x+2)3

A: using property of logarithmic

Q: 2 Solve log, (2 sinx) + log,(cosx) =-1, for 2n<x<-

A: According to Bartleby's guidelines. We are allowed to solve only 1 question ata time. Apologies for…

Q: A Logarithmic Identity Show that

A: We have to show the logarithmic identity: -lnx-x2-1=lnx+x2-1 We know the property of logarithmic,…

Q: 3. Use Log Rule to integrate. a. Sor5 Sdx а. бх-5 b. S; -dx x(lnx)²

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Q: If x2 + y2 = 25xy . Then prove that 2 log(x+y) = 3log3 +logx + logy

A: It is given that x2+y2=25xy add 2xy to both sides  x2+y2+2xy=25xy+2xy using the formula…

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: Show that 3x2 + log2x2 is Theta(x2). log2x is log base 2 of x.

A: Consider 3x2+log2x2 . It is known that  log2x2&lt;x2, for all x&gt;0. Then, log2x2&lt;3x2 for all…

Q: Obtain all values of ln (−4)

A: ln(-4)

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

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

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Q: Use these formulas to express the numbers in Exercises 61–66 interms of natural logarithms.61.…

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Q: () N f(x) = , show that f(0) and its leading differences form a geometr 5. (i) Prove that A log x…

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

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

A: Use property of log

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

A: We have to find the expansion

Q: 4 In x + In(x - 25) is the base e logarithm of

A: solution:-

Q: Use a graphing utility to evaluate the logarithm by the methods given below. (Round yol In(29) (a)…

A: Answer

Q: 8. Let a be a positive real number not equal to 1. Determine the solution of the equation log, (2x +…

A: To determine the solution of the given equation.

Q: In LRT reject H, when Ais small, so we reject Ho when the value -2 log A is small Select one: True…

A: Answer : False

Q: Use the properties of logarithms to write the expressions in Exercises 43 and 44 as a single term.…

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

Q: Show that J log(1 + tan0)d= log2

A: Given that: To prove:        ∫0π4log(1+tanθ)dθ=π4.log2

Q: 4. Show that id 5D accuracy is required to calculate the value of log(1+x) at x=0.1,0.5 by using the…

A: Given equation is log1+x=x-12x2+13x3+.....+-1n+1nxn+Rn+! So, Rn+1=-1n+2n+1xn+1 So, maximum relative…

Q: What will the coefficient (x – 1)² in the expansion of loge x about x = 1 ? %3D

A: Introduction :

Q: If Ptiq a %3D prove that log ay") a lap + Ba) %3D

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Q: 4. (a) Use logarithm properties to expand In ( (@+5)(x – 6)² (x+ 3)3). (b) Rewrite log3(x) + log3 (y…

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Q: (a) Use the definitions of hyperbolic functions in terms of exponentials to prove that 8 cosh'x cosh…

A: a) LHS =  8cosh4x  =  8(cosh2x)2  =  8 * ((1/2)( cosh(2x) + 1))2  =  2 (cosh2(2x) + 2cosh(2x) + 1)…

Q: 9.5. Show that (a). Log(1+ i)? = 2L0((1 + i) but (b). Log(-1+i)² + 2Log(-1+ i). %3D

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Q: Practice 5.10 Question #10

A: If  log x  =4, log y = 5, log z = 3, Using  properties of logarithm find the value of

Q: The table shows corresponding values of x and y obtained experimentally. By drawing a suitable graph…

A: Estimate the logarithmic values of x and y. Tabulate the values of x, y, log10x and log10y.  x y…

Q: . if võ =o, i =1 and Ju = 2 estimate 13 %3D by constructing Logrange polynamial, Itn with the exact…

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Q: Find all vawes of k don uhich log kx 112 log (x+) has one soluhion

A: Just use basics of logarithm.

Q: Solution to the equation Log(2iz + 1) = in is None of them z = ni z = i

A: Usually, log x is represented as log10x . If log x=y , then x=10y .  The natural logarithm, ln x is…

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

A: Given,           logx4y5

Q: a) log2 25 – log, 5 is the base 2 logarithm of ) 4 In x + In(x – 25) is the base e logarithm of

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Q: Expand loge x in powers of (x- 1) and hence evaluate log, 1-1 correct to 4 decimal places.

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Q: d log, x = 1 dx [(In a)(x)]

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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: 3. Solve the natural logarithmic equation. 3 In In x + In In 2 = 4

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Q: Use these formulas to express the numbers in terms of natural logarithms. 61. sinh-' (-5/12) 63.…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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

A: