1.) Evaluate the following: a.) ln 1                                    e.) log 1 b.) ln e                                    f.) log 10

Q: Does f(n) Is an element of 2^O(log2(n)) mean that f(n) is an element of O(n)? Why or why not?

A: Big -oh notation : Let us consider two function f  and g  on naturak numbers then f(n)=O(g(n)), if…

Q: Consider the function f : [0, 2 + e) → [1, 11) given by 2+ 6x – x2 if x E [0, 3) f(x) = 1+ In(x – 2)…

A: We will show the following result

Q: Which of the following represents the domain of h(t)=−log(x)+3?h(t)=-log(x)+3? (0,∞)(0,∞)…

A: We have to find the domain

Q: Show that loga b logb a= I for all a, b > 0 such that a # 1 andb #1.

A: We will use the change of base formula

Q: H-w/ prove That: の legiキ2109i @ log (i+i)=2 loy (iti) logそキ2 \ogz }2こメう

A: (1)

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…

A:

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: Find the largest integer n such that log* n = 5. Determine the number of decimal digits in this…

A: Given, the function         fk(n)=n               if k=0f(f(k-1)(n)) if k>0.

Q: i3m (a) Find all z such that log:

A:

Q: Which of the following is correct ? Olog 1 = nni, n = 0, ±1, ±£2, ±3, ... ... log 1 = 2nri, n = 0,…

A:

Q: Suppose f : R → R and g: R+ → R are defined by f(x) = x2 + 1 and g(x) = log x – x². What is go f? O…

A:

Q: If log, 3 = 0.7925, log, 5 = 1.161, and log, 7 = 1.4037, then the value of log, V21 is O 2.2767 O…

A: Given: logb3=0.7925 logb5=5.161 logb7=1.4037

Q: Let b be a real number satisfying b> 0, b# 1. Given that P, Q, R, and S are positive real numbers…

A: Logarithmic property: - Properties of logarithms functions are used to solve logarithm issues in…

Q: Show that, log(-1+i)² + 2log(–1+i).

A: Use the formula logz=lnr+iθ. To find log-1+i2:…

Q: 4. Determine whether each of the functions log(n + 1) and log(n²+ 1) is O(log n). 5. Arrange the…

A: We say f(n) = O(g(n)) or f(n) is O(g(n))  if and only if there exist positive constants  c and n0…

Q: - Tuncuon j(x) = xlog x , then f'(1) is a) 1 b) logx c) x d) None of these O d O a O c O b If f(x) =…

A:

Q: The Gutenberg-Richter Law states that the number, N, of earthquakes per year worldwide of Richter…

A:

Q: Show that loga b logb a= I for all a, b > 0 such that a ≠ 1 and b ≠. 1

A:

Q: Let f R*R, defined by f(x) = 3*, then f(x) = %3D O log,3 3* o log3x log3

A: See solution below.

Q: what is the log trans formed. form of t

A: Given,         V=aPb

Q: and the range is The exponential function f with base b is defined by f(x) = , b>0 and b 1. Using…

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…

A:

Q: snip

A: Prove that: logaMN=logaM-logaN, where a, M and N are positive real numbers and a≠1

Q: H.a/ prove that O cos2: log (2 ite) log (27f2-1)

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

Q: Find the principal values of each & express the result in rectangular form: 1. (- j) raise to j 2.…

A: (As per bartleby guidelines, for questions containing multiple subparts, only first three subparts…

Q: O Give a big-O estimate for f(n) = 3n log(n!) + (n²+ 3) logn.

A: Big O notation is a mathematical notation that describes the limiting behavior of a function when…

Q: Show that loga(M/N) = loga M - loga N, where a, M, and N are positive real numbers and a ≠ 1.

A: Here given equation loga(M/N) = loga M - loga N

Q: Select all of the following that are equivalent to 1, for all natural numbers, n. A. O (1)! В. О B.…

A:

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

A:

Q: Prove that log b (a ^c)=c log b(a)

A:

Q: 2. Determine all possible values and give the principal value of the following numbers (put in form…

A:

Q: Determine the O-class of the function h(n) defined by if n = 1 h(n) |h(L)+h([1) + log n if n > 1

A: We will first do a clever substitution to convert the given piece-wise function into a recurrence…

Q: (d) Write down the definition of the complex exponential, and using this prove that (e*)" = en=…

A: (d) To prove ezn=enz, n∈ℤ,n>0 and z∈ℂ

Q: Given that log a 2, logy 3 and log z = 4 find log () %3D %3D O 13 8. 7 O11

A: given: we have to find the value of .

Q: 10. Use the definition of a logarithm to find the exact solution for 4log(2n)–7=-11

A: Given, 4log2n-7=-11 To find the exact solution of above expression.

Q: The exponential function f with base b is defined by f(x) =_______ , b > 0 and b ≠ 1. Using…

A: Solution is below

Q: 7. Use log, 2 0.4307 and log, 3 0.6826 to approximate the value of log, 12. O A. 1.5440 O B. 0.8681…

A:

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=…

A:

Q: Find the value of log(-2). o 0.3 + 1.364i O -0.3 - 1.364i O 0.3 - 1.364i O -0.3 + 1.364i

A:

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

A:

Q: Number 2

A: To Evaluate: cos2(2-i)

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: 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: If a,b.c are in G.P. are log, a, log, c, log, bare in A.P., prove that the 3. common difference of…

A: Given that a,b,c are in G.P. And logca,logbc and logab are in A.P. we have to prove that Common…

Q: The natural exponential function f(x) = e", has domain and range as: O Range = R and Domain = (0,3)…

A: Domain : Domain of a function is the set of all values that can be plugged into a function and have…

Q: Let & be an exponential Define n=2+3Ě, and find: a) P(E>2). b) Mŋ and varn. c) P(E>2|n<11). r.v.…

A: For an exponential distribution  assuming the standard form, answer is given below