15. Solve each equation for x. b) 9*-1 = 31+ c) In(x+4)+ln(x-2) = 0 l+x a) e2" = e¤²–3 d) log +log 3 = log 15–log(x+4).

Q: 9. 8 logx 4. -2 - 3.

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Q: 3

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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: Given that log4(y-1)+log4(x/2)=z and log2(y+1)+log2x=z-1, Show that y2=1+8z and find the possible…

A: Concept: Logarithm base change rule: logb(x) = logc(x)  logc(b) Logarithm quotient rule: logbxy=…

Q: 9. 8) logx -2 4. 3. I|

A: we have to find logx34=-23

Q: 1-In (-) + In(2x) = In3 2- 4 log 2 - log3 + log16 = x 3-Expand In [x? sin x /Vx2 +1]

A: To find the value of x

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

A:

Q: Determine the maximum and minimum values of the function f(x)= -4 x log2x on the interval [1,4]

A:

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

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Q: Express th equation in exponential form.

A: a). Given, lnx+1=2 The exponential form is, x+1=e2         ∵lnx=y⇒x=ey⇒x=e2-1

Q: 2. Differentiate: a) y = log2(3x) %3D 2 b) f(x) = –7 log(x²) %3D

A:

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: e3+j4(3+ j4)5 log ji' sin(3 + j4) j2022

A:

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

A: Answer

Q: 10. Prove that (log2 3)-1+ (log4 3)-1 < 2.

A: Simplify the powers of the term (log23)-1+(log43)-1 by writing the terms as fractions.…

Q: B. Express as a single logarithm and, if possible, simplify. 1. log, x + 4 loga y – 3 loga x 6.…

A: This is a problem related to logarithm properties. Based on the general formula we can answer the…

Q: 3) In x-log x = 1. Answer should be in the natural exponential form. %3D

A: This is complicated and lengthy problem, so I can do it in Advanced Mathematics.

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

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

Q: (b) 5" (2 – cot 5")(1 – csc 5“) dx SC 11 – 2 log x (c) / dx JIV6 log r – logʻ 1 x/6 log x -

A: You have asked Only part b and c

Q: 14. Find the domain of definition of the function 31 Vx + 5 X-5 y = log10 (,2 x² – 10x +24

A: The domain of a function is the set of input or argument values for which the function is real and…

Q: a) In (x – 7) = 6 (b) In (x + 9) + In (x- 9) = 1 (c) log sx - log 52x = 2

A:

Q: 1. In 2x - 21n/2y³ + In(xy)² as a single logarithm.

A: since you have posted multiple question i can do first question as per pur company guidelines please…

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

A:

Q: #12. SOLVE THE EQUATION а. log (x²) = (log x)² 1 or 100 b. log Vr – 9 = 2 V 10,009 С. log (x³) =…

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: 19. If log,2 = x and log34 =y, then log372, in terms of x and y, is equal to O 2x +2y O 9x +9y O 9xy…

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Q: I need some help on ii for #1 please!

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

A: Property of logarithm

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

A: See the solution step by step.

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

A:

Q: Determine the maximum and minimum values of the function f(x)=-4 •log 2x on the interval [1,4]

A: Given function is  on interval [1, 4].

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

A:

Q: Without using log tables prove that 1orsid ei boeu ss to 16 +12 log10 15 25 +7 log10 24 81 = 1 80…

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Q: 4 In2 log2 x 1-

A: At first we will change base of log2x to natural log by using base change formula. Then use…

Q: Express th equation in exponential form.

A: (a) Given expression is log35=x. Express the above equation in exponential. logab=c, then…

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

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Q: Use values of f(x) = In(x) %3D to estimate log ( 6.67 ) using 4th order

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Q: 4. Show that sinh-1 x = log(x + vx² + 1).

A: We have to prove the result.

Q: 8. Solve. Give EXACT answers only- (a) e**1 = ! %3D (b) 3log2(x – 1) = 5 – log24

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

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Q: 13 1. Solve 2 log, (x + 4) – log2 ( 2.x + 2 = 1 -

A: Given,2log2x+4-log22x+132=1 Used Properties: 1. logaxy=ylogax                            Power…

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

A: