T + log, (V2" . 2™ sin 24-1 (-1)5 + (–1)27 (-1)766 3 25 – 24 – 23 + log, (log3(915) + 71+(-1)17 + 1) + 23/2

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

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Q: 1. lim (2*+5 - 7) 6. lim (ln3x -- 8) - 7 X-5 x--3 2. lim (22x-1-3) 7. lim log2 (x² + 4x + 4) w X-3…

A: 1) Given:                  limx→52x+5-7 Plug in the value x = 5                 =25+5-7=210-7=1017…

Q: (d) In 3 – In x – In(x+ 5) = 0 (f) log2(x – 1) – log2(x+3) = log2 ) (e) log,(x + 2) – log,(x – 1) =…

A: Given d ln3-lnx-lnx+5=0e log4x+2-log4x-1=1f log2x-1-log2x+3=log21x

Q: snip

A: To prove,  loga1N=-logaN where, a  and  N are positive real numbers and a≠1. Now, take the left…

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: 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: (iv) log, r – log,(r – 1) = ; (v) 41-z = 32r+5 () -- (vi) 2x In = 0

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Q: 2. The function f(x)= log₁0x has the point (10, 1) on its graph. Find the coordinates of the image…

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Q: Example 2.32. Using Newton's iterative method, find the real root of x log10 x = 1.2 correct to five…

A: Newton's method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to approximate…

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

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

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

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Q: 10- 11- 12- In 2 log₂x X 2 log10 (x + 1) x + 1 dx x log10 x 0 S -dx -dx

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Q: 1. The solution to the cquation 53x = correct order on the right of the question. 4x+1 is given…

A: Re arranging steps in correct order,..

Q: log31 = logo(1- 4x) log(3x- 2) 5 log, y +5 log2 4 log x = r(x) %3D h(x) = logs 3+x

A: Given: We have to identify the given as function, equations, and inequality. The function can be…

Q: #11

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Q: Write each expression as a single logarithm

A: Given,

Q: valuate. Express result in Rectangular Form correct decimal places. z = log(1-5) (2 + 4i)(1-2t) +…

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Q: f (x) = In(x + 4) + 3 %3D f(2) 3 e2-6- 4 %3D f (x) = log(a- 2) - 8 %3D f (x) = 108+2 ----- f (x) =…

A: Some functions are given and the inverse of the functions are also given. We have to check that…

Q: 4. Determine the co-ordinates of the point of intersection of the graphs of f(x) = 5(3*) %3D log a…

A: The given curves are  f(x) = 5.3x f(x) = 7.2x

Q: Q1: Find with sketch the Fourier coefficients and Fourier series of the function f(x) defined by…

A: Introduction: A Fourier series is a sum of sine and cosine waves that represents a periodic…

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: Log 2 = 0.301, log 3 = 0.477,  log 5 = 0.699 and log 7 = 0.845 Using this information only, find:-…

A: According to the given information, The given log values are:

Q: 2 lim log 10* X-1 8. -3 lim log,(x-2) x-9 А. 3/2 В. 2/3 C. 1/3 D. DNE

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Q: 7. log;(x²) =, x log5(_ 8. log,(y*) = x log-(. 9. log(V1000) = – x log( %3D

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Q: Find odd and even function (half range) Fourier series of function below f(x) = { Osxs1 |1<x <2 2 -x

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Q: 7 log.y- log, w+4log.z 5

A: on applying log algorithm we will get

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: 2. In (x + 2) + In 2 = 3 | 4. log:9 – logs (x+ 10) = 1 6. log, (x² +3x) – log, (x + 5) = 1

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Q: Find a real root of 3x – log10 x – 8 using the Successive Approximation method. Correct to four…

A:

Q: Q1 finel fourier series F(x) = 2-

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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: Find odd and even function (half range) Fourier series of function below 0 <x<1 1< x < 2 f(x) = {…

A:

Q: 4. The expression log(sinx) – log(cos.x) , 0<x<, is equal to A. log(sin x cos x)

A:

Q: 1. Given that z=8-6i, write its exponential form. Round off decimal answers up to 3 decimal places.

A: Here, a=8b=6

Q: 1. Problem. Express the function f(x) e"/L (for 0 < x <L and assumed to be periodic with period L)…

A: Given:- Express the function f(x) = ex/L (for 0 ≤ x ≤ L and assumed to be periodic with period L) as…

Q: Some biorlogos model thenumberof S species in afixed area A (e.g. an island) with therelationto…

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Q: 4. Express the following single logarithm: as a i) log3 54 -log3 6 ii) 2 In (5a’b) – In (125 aº b²)…

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Q: Explain some of the similarities and some of the differences between using a Laplace transform and…

A: Suppose we choose  1) laplace transfer 2) successful approximation method     1) Laplce transform…

Q: log base 3 (x+3)+log base 3 (x-3) = 3

A:

Q: 1. Prove that (i) Log i = 2 (ii) Log(-5) = ln 5 + ti %3D i) = 3 In 2 + 2 (iv) Log(1+i) = In 2 + 3ri…

A: Since you have posted multiple questions, we will solve only first three parts of first question for…

Q: 1. y = -3+log, r 2. y = log, (r – 2) 3. y = - log, (æ + 3) 4. y = 2 + log,

A: we have to match

Q: rewrite each expression as a singlelogarithm.

A: 35). Given expression is 3log2x+log2y To rewrite the expression as a single logarithm. Solution:…

Q: 5-Solve a) log3x + log3(x + 6) = 3 b) log10 (3x-2) -2log10 X+1 = 2 c) log, (1– x) + log,(2x– 5) = 3…

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

Q: 12 %3D 5. (i) By using the substitution u = 1+ cosh x, rcosh-12 tanh x dx, 1+ cosh x evaluate…

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Q: log,(x – 5) + log,(x + 3) = 1 In(5x) + In x = In(100) In x + In(x – 1) = 10 In(x + 25) – In(x – 1) =…

A: