Use the following steps to prove that log(xy)= logbx+ logby. a. Let x bP and y = b. Solve these expressions for p and q, respectively. b. Use the property b*bV = b**"y to express xy in terms of b, p, and q. c. Compute log (xy) and simplify. + b a. Let x bP and y b. Solve these expressions for p and q, respectively. q = (Simplify your answers.)

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

A: Given: prove that ddxlogax=1xlna We know that logpq=lnqlnp…

Q: evaluate the Following 'F log p = X and log q=y, x and y. In terms

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Q: Given that log x -3 and log y = 5, find log Vy.

A: The given expression is logx2y35 and logx=3   and   logy=5

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Q: Apply the formula deduce that (x) log x + [A(n) () = 2x log x + 0(x) n n≤x as x→∞o, where y is…

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Q: use the following steps to prove thatlogb xy = logb x + logb y.a. Let x = bpand y = bq. Solve these…

A: We have to prove logbxy=logbx+logby by using the given steps .

Q: Find the inverse 2-Transforrm of log(z f log 241 by Power senies method and by division method

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Q: The domain of definition of Rx) = /log (log x)- log (4- log x)- log 3 is %3D (b) [10°, 10*] (d)…

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Q: Suppose log, (3) = m, log„(5) = n, and log.(7) = z. Find the following: %3D 25 a) log.(15) b)…

A: Given: loga(3)=mloga(5)=nloga(7)=z

Q: If loga = logx – 2(logy + logz), then a is equal to O Ax-y²z? В. Х v²z? O C.x-2y+2z OD. X 2y +2z

A: given,

Q: Given that log 2 = x, log 3 = y and        log 7= z, express the following expression in terms of x,…

A: We will write 0.3 as fraction. That is 3/10

Q: Denote by Log(2) the principal branch of the complex logarithm, and let +y be as in Exercise 4.…

A: To solve the given problem we use the  defination the residue of  pole and find the integration with…

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A: We need to find S(33). S(33)=325+500log(100)

Q: Evaluate the following: log, a Find y in terms of x for In(y+1)=2– 3 In.x

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Q: Which of the following are equivalent to log 4+-log x-5 log y? Select all that apply. 3 1 log 4+ log…

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Q: Evaluate the following using a method of your choice. ( JY a) log, 625 = b) log,2 + logʻ32 =

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Q: 1) Condense the following logarithr 4log3x + log,v 2) Expand the following logarithm log.()

A: We have to expand logarithm

Q: Which of these are equivalent to log(5r)+ log(3x)? Select all that apply. O log(15z) O log (152*) O…

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Q: Express the following as a single logarithm and, if possible, simplify. log a(c - d) + log a (c + d)…

A: we have given logarithmic expression  And we have simplify.  For this we can use the properties of…

Q: Determine the expanded form of the following log expression log5(x^-7y^5/z^10)

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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: 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: Given that log 4 x = 2 and log 2 y = 3, evaluate x / y. Select one: a. 1 b. 3 c. 2 d. - 22

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Q: Use the properties of logs to expand: x+5 b) log+ 3x-2 d) log, x(x + 4)

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Q: Suppose the functions f, g, h, r and I are defined as follows: f (x) = log+log x 3 g(x) √(x+3)² h(x)…

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Q: Verify that for all x, the change-of-base formula holds: loga x for a,b > 0 such that a # 1, b 1.…

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Q: Determine the numerical value of the following expression without the use of a calculator: T + log,…

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Q: Define the variables x and t as x = 2.56, and t=6.7, then evaluate: a) 2x4 – 6x3 + 15x2 + 12 e 2x b)…

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Q: A/Certain values of x and log1o x are (300, 2.4771), (304, 2.4829), (305, 2.4843) and (307, 2.4871),…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Expand the log by using the properties of log.

A: The given log function is,

Q: Which of the following expressions is equivalent to log(3) - 2 log(2x) + 3 log(y2) show your work…

A: Using logaritms formulae loga+logb=logabloga2=2logaloga-logb=logab We have given log3-2log2x+3logy2…

Q: Which of the following is equivalent to log( V2x+y ? (2x+y) O In (In(2x+y)-3 In y) In 10 In(2x+y) 3…

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Q: 51. Verify that for all x, the formula log, x = loga x - for a, b > 0 such that a + 1, b 1 holds.…

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Q: 3. Write the following expressions in terms of logs of x, y, and z. c. log xy2 a. logx²y b. log. z8

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Q: Condense the following log expression. -2log3(xy)+4/5log3(z)^10+log3(x+1)

A: Condensing the logarithmic expression.

Q: 2. Given p = 2' and q = 2', express log, p'q in r and t terms. 64

A: Given

Q: Condense to a single logarithm. 3 - log 8 (m) – 2log8(4n) – 31og 8 (5k) 5 log (4n)² (5k)³ Vm³ log s…

A: Solving the problem by finding the given expression to a single one.

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: B. Find x if log 4 + log x = 2.3 %3D 195.52 49.88 O27.98

A: In this question we have to find the value of x which we can find out by using the property of…

Q: Use the Laws of Logarithms to expand the expression. xy (а) log x + 2 (c) log V + 4) (b) In

A: We know that, the property of logarithm is given as logmn=nlogm                 ⋯⋯1logmn=logm+logn…

Q: a, logioo[To] b. log 625 C. log 64 d. log Lio01] e. logg! f logm vo 1 log, 2 ho logz 7 t.

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Q: Suppose the functions f, g and h are defined by 33 f(x) = 3* + and g(x) = log̟ x + log̟ (x + 6) + 4…

A: In this question, we find the domain of each of the given function f(x), g(x) and h(x). In other…

Q: Given that: toge C4-1)+ Log4 )=Z and Log, Cyt1)+LogE2= Show that 42-1+8² and find the Pessible…

A: We are given: log4y-1+log4x2=Z⇒log4(y-1)x2=Z⇒4Z=(y-1)x2Now,Z=1⇒(y-1)x2=4⇒(y-1)(x)=8 ---(1)Also we…

Q: Differentiate each of the following functions. b. log to the base of 5 (the root of 3x) d. log to…

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Q: Express the following ratios as ratios of natural logarithms and simplify. log y a log 11 X log 5 x…

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