2. Determine all possible values and give the principal value of the following numbers (put in form x + iy): (a) i1/2 (c) log(1+ v3i)

Q: 13. Combine the following into a logarithm: single 2 log – 3 log y + log(x*y²)

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Q: .Expand log (1 + sin x) in powers of z as far as the term in r.

A:

Q: Solve the following logarithm problem for the positive solution for x. 1 logr 9. 23

A: Logarithmic properties.

Q: Solve the following equations for x (a) 31-x - 92x (b) log2(z – 2) + logą z = 3

A: On solving the first

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

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Q: 9.4. Evaluate the following: (a). Log(-ei), (b). Log(1 – i), (c). log(-1+v3i).

A:

Q: (22x + 2) dx 11 In|x² +4] +2 tan -1 x2 + 4 +C 2 Logarithm function is missing parentheses around its…

A:

Q: Solve the following logarithmic equation: z=7, k=3 log;(Z + 8)x7 – log3(2K +9)x³ = log;(Z + 5)x² +…

A: Given,         log3Z+8x7-log32K+9x3=log3Z+5x2+4Z+K-6         When Z=7 , K=3

Q: (1) solve the following  i) 2x/2-16  = 1/32  ii)  log8 (x-2) log8 (x )= 1

A: We have to solve and finding the value of x  Here using logarithmic properties

Q: 1 1 1 The value of log, n log,n SI- log,™ -+- t.

A:

Q: Which of the following functions grow faster than In x as xoo? Which grow at the same rate as In x?…

A:

Q: (1) Solve the following: (a) 42x-1 = 64 (d) In 3 – In x – In(x + 5) = 0 (b) 81–x = 4x+2 (c) 22x + 2×…

A:

Q: A function defined by y = ab can be written in terms of an exponential function base e as

A: The function is y=abx

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: Determine the numerical value of the following expression without the use of a calculator: *+ log2…

A: Consider the provided expression,

Q: (1) (a) Solve the following: 1 (i) 2*-6 8. (ii) log,(x+3) =1– log,(x-1)

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

Q: (-1,}). Find a formula for the exponential function passing through the points and (1,20) f(z) =…

A:

Q: (1) (a) Solve the following: 1 (i) 2*-6 (ii) log;(x+3)=1-log;(x-1)

A:

Q: 11) Given that log, 6= m and log, 5 =n, show that log, 10 = mn+m-1 %3D 12) Solve for x in the…

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

A:

Q: Suppose that when a certain lake is stocked with fish, the birth and death rates B and 8 are both…

A: (a)

Q: Simply the following 1 1.5 Inx – In(x² – 1) + 2ln(x + 3) 2. 5log2 + log3 – log8 -

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: (b) 8[log(2-j3)]e

A:

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

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

A:

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: 1-coth² (log₂x) dx x cosh(log₂x) 1. 11/20

A: We have to find the integral.

Q: Determine the numerical value of the following expression without the use of a calculator: T + log2…

A:

Q: Find the exponential function f(x)=a^x that passes through the point (3,343) and has a y-intercept…

A: We have to find the exponential function f(x)=a^x that passes through the point (3,343) and has a…

Q: 1. Which of the following functions grow faster than e* as x→∞? Which grow at the same rate as e"?…

A: Dear students,  Please find the solutions of 3 parts. In case you need help with the other questions…

Q: 2. Compute for the value of x in a given logarithmic inequalities loga(x+1) > log:(x2). a. x > ½ b.…

A:

Q: 4. Solve the following logarithmic equations: a) logx+log(x+15) =2 b) log,(x+1)= 1 +log, x d)…

A: We have to find value of x for given problem

Q: 2 Show that the following functions are harmonic in x and y: 2 log√x² + y²

A:

Q: 2. i) Now, on your calculators, compute the following: e-24 = log2 3 =

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Q: The solution of the equation Log(z² – 1) = in is

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Q: The human population x of a certain island satisfies the logistic law dx/dt = kx with k = 0.03 = 3 x…

A: GIVEN: k = 0.03

Q: 4. Solve the following logarithmic equation: log; (Z + 8)x7 – log3 (2K + 9)x3 = log3 (Z + 5)x2 + 4(Z…

A: Here, Z=9k=5

Q: thats a natural log of 9 to 0 and integral from 9 to e^x

A:

Q: 9. Solve the following simultaneous equations: logx+log(y²)=4 log²x-3log(xy)=-5 Where x,y are real…

A:

Q: 3. (a) Calculate sinh (log(5) – log(4)) exactly, i.e. without using a calculator. Answer:

A: Solution is given below:

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

A:

Q: 1. Express the following as a single log 3log xy-log x +log y a) 6log x b) 3log x c) 6log y d) 3log…

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Q: b) Find the value of x that satisfies log(x+3)− log x = log x+log 2.

A: Follow the procedure given below.

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

A: The logistic equation is given as dNdt=Na-bN and its solution is given as N(t)=aN0bN0+a-bN0e-at…

Q: 1. Find the natural logarithm of the following when z equals: 1. -10 ii. –3 – j4 jii. 0.6 + j0.8

A: