1.) lim In(4x) = 2.) lim In(x2 - 5) = %3D X→の 3.) lim In(x) = 4.) lim In(2x) = 5.) lim (-In x) = %3D

Q: ,2,3 Expand into several logarithms: x'y In 25

A: Logarithm is inverse of exponentiations. A logarithm is easy method to express large number and to…

Q: (h) lim - 7 log: (z) -0- ||

A: Given query is to find the value of indicated limit.

Q: Solve for x using sci notation x=log(y^5) ; if (log y) = 1.2 x 10^-4

A: We have to find value of x by using scientific notation.

Q: 3. Find syz for ys = In(x + yz) – xcoth-1 log ().

A: Given : Let us consider the given value as,  ys=ln(x+yz)-xcoth-1logzy

Q: Is ln xy = ln x ln y a valid property of logarithms, where x > 0 and y > 0? Explain

A: ln(xy)=ln(x)+ln(y) using the addition property of logarithm. Where x>0 and y>0.

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

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Q: let f(x)= x^5x where x>0. use logarithmic differentiaiton to find f'(x)

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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: 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: 06. lim, xcsc X 3csc 6x 07. lim,→x/2 csc2x e* +3x 08. lim, e* + 0.5x?

A: According to guidelines here solution of only firt 3 questions

Q: 5. Show that --I+#^) log, (V +1- x) + log, (VF+1+x) = 0 x². x² + 1 + x

A: We know the property of logarithm, logb(a)+logb(c)=logb(ac)

Q: For the Limits of Logarithmic Function, we should consider that limx→a ln g(x) = ln g(a) where g(a)…

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

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Q: X-y 19. If log 3 (logx + logy), show that x+y = 11r %3D

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

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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: 1 [log, (x- y) - log; (x+ y)]

A: Given that: 12log5(x2-y2)-log5(x+y)

Q: The number N(t) of people in a community who are exposed to a particular advertisement is governed…

A: Given that Nt represents the number of people who are exposed to a particular advertisement. The…

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: If f(x) and g(x) is any function then, If limx→∞f(x)g(x)=∞ then f(x) grows faster than g(x). If…

Q: Differentiate with respect to x:* y = log, (x) :() 2+ In x - In x Option 2 Option 3 2 - In x 1+ In x…

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

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: 2 -3 r- 3 x = %3D (z + 4)- 1 = 24 --- log, 15625 6 X = !!

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Q: dy : Prove that dx or ỹ for expression y log2(x²) is equal to ỹ = 2[1-log2 x² In 2] %3| x2 x³ In 2

A: Given, y = log2x2x2    We have to prove dydx or y¯ = 21-log2x2.ln2x3ln2

Q: Prove: logaxr = r loga x.

A: Given equation: loga xr=r loga x

Q: Evaluate the limit as x approaches infinity of log7x/log8x

A: We need to evaluate the given limit

Q: 54. For any positive constant k, the derivative of In (kx) is 1/x. Prove this fact (a) by using the…

A: Given for any positive constant k, the derivative of ln (kx) is 1/x. To prove that  a) by using the…

Q: 2. Evaluate [log(-1-1)(-2-j2)] tan(4 + 3i) cosh-

A:

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: Find the exponential functions of the form f(x) ab* that pass througl

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Q: 2log x-1=log(x-1)

A: Given:  2logx -1=log(x-1)we know that alogb =logba   then 2logx=logx2Then    logx2-1=log(x-1)…

Q: dy Find by first using algebraic properties of the natural logarithm dx (x+ 4)(x + 5)° In function…

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Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: fx=x2lnx gx=ln2x⇒gx=lnx2 limx→∞fxgx=limx→∞x2lnxlnx2limx→∞fxgx=limx→∞x2lnx

Q: 17. The product rule does apply when multiplying exponential functions with sinusoidal functions.

A: Yes the product rule applies when multiplying exponential functions with sinusoidal functions

Q: ive the logistic function modeling initial value = 6,   limit to growth = 20  and passing through…

A: Given, Initial value=6 Limit to growth=20 And passing through the point is (3,15) We know that the…

Q: 5. The natural logarithmic function f(x) In x has the %3D asymptote x %3D

A: Given function - f(x) = ln(x)

Q: How do I expand this logrithmic equation? In(x2 square root of y/z)

A: Given:

Q: solve for x, log(x+5)-log(x+2)=2 please show work.

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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: 2. Evaluate [log(-1-1)(-2- j2)] cosh- tan(4 + 3i)

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

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Q: 3. Find syz for ys = In(x + yz) – xcoth- log ()-

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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: What is the linear approximation of log base 5 x at x=5

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Q: The natural logarithmic function f1x2  ln x has theasymptote x 

A: Graph of f(x):

Q: Match the logarithmic function with its graph. I II y 1 + III IV 1 ++ (a) f(x) = -log2(x)…

A:

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

A:

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: We know that from the limit method, a function fx grows faster than gx if and only if limx→∞fxgx=∞…