Combine into a single logarithm. In(x – y) – 2 In(x² + y²) OIn (x-y)3 In (x²+y²)* In Va-y) (x²–y²)? On Va-y In (x²+y²)?

Q: 2. Ifƒ (x, y) = log (x² + y²), then ƒ +ƒ is equal to XX yy 1 (a) x² + y² (b) 0 1,² - x² (c) (d) *…

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Q: (ii).Given that log, (y-1)+log, = z and log, (y+1)+log, x= z – 1, Show that y = 1+8° and find the…

A: Given: log4y-1+log4x2=zlog2y+1-log2x=z-1 . . . . . (equation 2) Concept: Here we shall use the…

Q: pmogeneous a²u ду? du a. (y + 2)² – 2x log y + k - In u = 2e¬*, k > 0 ax? ду b. и хх + ху иҳу + y?u?…

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Q: Condense each logarithmic expression.

A: We have to condense the following logarithmic expressions -  (a) 12log x + 3 log(x+1)⇒ log(x)12 +…

Q: 4. Find the value of x in each of the following (convert to exponential form to help!). a) logX = 2…

A: Note:  Hello User, as per company policy we should answer only for first three subparts of the…

Q: ) f(x) Log2 x ,x= 32 b) F (x) = Log3 x , x=1 c) f(x) = Log 4 X, x= 2 d) F(x) = Log10 x, x= 1/100 e…

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

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Q: (b) Show that u(#) = log log (1 + l#|") belongs to W(U) but does not belong to L(U).

A: Given: u(x)= log log(1 + |x|^-1 )

Q: b) Expand log(a+h) by Taylor's Theorem.

A: Consider the expression: loga+h ……1

Q: i) log, (5x + 4) – log,(4x) = 2. ii) 9e* + 4e-x – 12 = 0.

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Q: 1) Solve for x and y in the following simultaneous equations *a) log, x = 2; 5y= x +12 log, y *b)…

A: We have to solve for x and y in the following simultaneous equations.

Q: Condense 2. Conden se into a single logarithm. 2) log x+log y+ 3log z O a) logxyz3 O b) log(xy/z³) O…

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Q: Find y by logarithmic differentiation. y=x²X A O y = 2 In x+2 2 In x-2B O y = x²* (2 In x+2) .C O y…

A: Use log to differentiate

Q: 2. Expand the following natural logarithms: In(zx'y") b. In- zy а.

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Q: 4 log, (x) – log, (x² – 2x) Condense

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Q: - Use the fact that d In x/dx = 1/x, as well as the change-of-base theorem for logarithms, to prove…

A: Given : d lnxdx = 1x d logaxdx = 1xlna

Q: Given that y = log, 11 and 64 %3D x = log 2, what is logp expressed in terms of x and y? a. 2х-бу b.…

A: We are given that y=logb11 and x=logb2. We need to find what is logb64121 in terms of x and y. Now,…

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: (b) An elementary charge is 1.602107 log (1.602 x 10-19) - 19 A Ć. Approximate log (1.602 × 10-1⁹).…

A: I have appended the formula used in the solution part of the question

Q: Express log b in terms of logarithms of x, y, and z. y'z Choose the correct expression below. А. log…

A: We have to express in terms of logarithms

Q: A linear relationship between the logarithms of the variable x and y which are connected by the…

A: We Know that Logarithmic Rule, log(ab) =log(a) +log(b) log(an) =nlog(a) By using above rule we find…

Q: (b) Show that u(2) = log log (1 + la|") belongs to W12(U) but does not belong to L (U).

A: Given: u(x)= log log(1+|x|^-1)

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: Condense to one logarithm: 7 log4 x – 6 log4 Y + 5 log4 z Which answer is correct? (A log (7x + 6y +…

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Q: Solve for x. (a) In (x – 3) = 7 (b) In (x + 4) + In (x - 4) = 1 (c) log gx² - log ,2x = 3

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Q: 2. Express the indicated logarithm in terms of a, b and c with the assumptions that log 2 = a, log 3…

A: To express the indicates logarithms in terms of a,b and c.

Q: given that ln 2 = x, ln 3 = y, and ln 5 = z, express each of the given logarithmic values in terms…

A: Given:   ln 2=x , ln 3=y, ln 5=z   To find:   The logarithmic values in ln 30 in terms of x, y, z…

Q: - y =log x² dy_ 8log, x A. dx dy 4log, x В. dx dy _ 4xlog, x xIn 2 dy 8x log, x D. dx xln2 xIn2 dx…

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Q: A3. (a) (i) Express 2ln x – ln √x as a single log in its simplest form.[

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Q: Models For each of the models listed below, predict ywhen x = 2.a) ln yn = 1.2 + 0.8x d) yn = 1.2 +…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: (a) f(x) = log,(log3 x) (b) g(x) = log [In(x – 1)] (c) h(x) = ln [log(æ – 1)] (d) j(x) = log [log…

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Q: 37. Express log b = 16x²vz* in expanded form. %3D V(x-13 A. Log b16 log bx²y log bz-log b (x-1)² B.…

A: We have to apply logarithmic formula

Q: - f(x) = - f(x) = x-2 g(x) = 5 In x - 2* g(x) = 4x' log, x %3D f(x) = 10* · e*

A: Solution of question is written in below steps.

Q: Which of the following are equivalent to 5 · log (u-1/6)? Assume u > 0. 1 O log log (u/") 1 log (u")…

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Q: x- log, (x – 6) = log , 9 4) log, (x– 10) + log, 4 = 3 %3D g7 g, (x + 3) – log, x = 1 6) log, 8 +…

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Q: Let ln 2=a , ln 3=b, and ln 5=c. Express the following logorithms in terms of a,b,c.  a. ln 4000=…

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Q: Find d (7ª). Type In(x) for the natural logartihtm function. dx

A: Given query is to find derivative if the expression.

Q: If log a= x and log b= y then log (ab^2) equals 1/2(x+y) x+1/2x+22x+2y

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Q: Verify the formulas d -[a*] = a* In(a) dx y = a* log,(y) = x. starting with let and the fact log,…

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Q: Given that log2=x, log3=y, and log7=z, express log15 in terms of x, y, and z.

A: Given that, log2=x,  log3=y,log7=z The objective is to express log15 in terms of x, y, and z.

Q: 4. Condense the log to a single log expression. a. 2 log y - 3 log x - 2 log 10 b. Ina+3 ln y

A: See this solution in below

Q: Differentiate y = 3e +7 ln(2x) + log, x- 4" O y' = 15e5 ++ 1 - 4* In 4 %3D - I In 2 O y' = 15e5-1 1…

A: We have to differentiate  y = 3e5x + 7 ln(2x) + log2x - 4x.

Q: Find the domain of each fucntion: a.) f(x) = ln(2-x) b.) f(x) = log2(2x-3))

A: Calculation:Note that the argument of the logarithm function always positivea.) The domain of the…

Q: 1. solve for x, log2(3x-2)=4.    2. use the laws of logarithims to rewrite 7log x - 3log y as a…

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Q: (a) f(t) = In(5t - 4) 12 (b) g(x) = log(x² - 25)

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

A: According to our company's guidelines I can only answer first three subparts of the question B since…

Q: b) Given that log, (y-1)+log,|| |= z and log, (y+1)+log, x = z-1, Show that y? =1+8² and find the…

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Q: 16 24 8 log. Z. to

A: Given logay16z24x58

Q: 2 log3 (x) + + log3 (y) is equivalent to: 2 log3 (ry) O log3 (2ry) O log, (2*y) O log, (zy)

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