4. Solve the following congruence, using the tables of discrete logarithms (next page):3x^9 = 6(mod31) The Prime 31 N 0 1 2 3 4 5 6 7 89 I 0 1 2 3 4 5 6 7 8 9 0124| 1|18|20이25|28|12|2| 114 23 19 11 2221 6 726 4 2 8 29 17 27 13 10 5 316 9 315 1|3 927 19 26 16 17 20 29 1 25 13 8 24 10 30 28 22 4 12 5 15 14 11 2l 618 23 721 012

Q: Which of the following statements is equivalent to the statement: 17x=83521 a)…

A: We have to convert the exponential expression to logarithmic expression.

Q: One of the following is False: Log(-) = Log(z1) – Log(z2). %3D 2 log(z1z2) = log(zı) + log(z2). %3D…

A: In the given question we have to choose the correct options from the given options. we will solve…

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

A:

Q: Simplify the expressions in Exercises 65–68.

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Which of the following is equivalent to In(2x – 3) = 5 e2x-3 = 5 %3D e = 2x - 3 %3D log5 e = 2x - 3…

A:

Q: Estimate the natural logarithm of 2 using linear interpolation. First perform the computation by…

A: We need to use linear interpolation to approximate ln 2 by varying the interval length.

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

A: Given that  (i) y log2 8 = x and 2x + 8y = 8192 (ii) log2x + 2log4y = 4 and x +12y = 52 Here we have…

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

A:

Q: One of the following is False: elect one: P Log(z12) = Log(z1) + Log(z2).

A: Log(z1*z2) = Log(z1) + Log(z2) is not necessarily true for all complex z1,z2.

Q: Find the value/s of x in the following equations/inequalities. 1. log3 (x+ 4) = log3(2x – 4) 2.…

A: As per guidelines we can solve only one question at a time, so the first question can be solved as…

Q: Consider the following “proof”. 3 > 2 3 log 0.5 > 2 log 0.5 log(0.5^3 ) > log(0.5^2 ) 0.5^3 >…

A: Topic :- Logarithms

Q: 4. Prove that for positive arithmetic functions f and g, din din Hint: Take logarithms to get the…

A:

Q: [2.5 b. Let A = | 17 [8 In1 + log100] C = and D= Lesor and D = Lcsc90° Find the following: If B²…

A:

Q: If x'8, 18 = y" 12 18 = Z ', prove that 3,3 log, x, 3log, y,7 log, z from an A.P. %3D

A: Given:-  If x18=y12=z18,  To Prove:-   3logyx, 3logzy, 7logxz from an A.P.

Q: One of the following is False: Select one: O Log(21z2) = Log(z1) + Log(z2). %3D Oi elogz = z if z #…

A: Log(z1z2) = Log(z1) + Log(z2) + 2nπi n = 0, 1, -1

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: 14. Given prime p := 8901577, primi Discrete Logarithm Problem via

A: Given: Let the prime p = 8101 And generator of Z8101 in a=6

Q: One of the following is False: Select one: o Log(z122) = Log(z1) + Log(z2). %3D O dogz = z if z# 0.…

A:

Q: 1. Which of the following is not equivalent to log 367 (1) log 2+log18 (3) log 30+ log 6 (2) 2log 6…

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

Q: One of the following is False: Gelect one: O Log(z12) = Log(z1) + Log(z2). %3D Pi dogz = z if z ± 0.…

A: one of the following is false

Q: One of the following is False: Select one: O Log(z12) = Log(z1) + Log(z2). Oi elogz = z if z # 0.…

A: Solution:

Q: 16 of 25 Condense to a single logarithm. 3 log 8 (m) – 2log 8 (4n) – 3log 8 (5k) 5 log (4n)² (5k)³…

A:

Q: If told the log 3=which of the follow is correct Log 27=0.477+0.477 Log 27=0.477x0.477x0.477 Log…

A: log(xn ) =n log(x).

Q: Match the Following: If Int – In 7 = 1 then t = Choose. If log z + log 5 = 1 then z: Choose. 23.15…

A:

Q: Consider the following LP Min z = 3x, + 2.x, +7x, s.t - x, + X, =10 -2x, + x, - x, <-10 *,X,,x, 2 0…

A: Hi! As per norms, we will be answering the first question. If you need an answer to others then…

Q: Prove that log(x + y) = log(x) + log(y) if, and only if, y = 1, where x > 1.

A:

Q: For which value(s) of k, if any, is the function 1 (²) = x [kx² - log₂ (x) 2xk²x + 5 continuous on…

A: Use continuity definition of function

Q: Find all vawes of k don uhich log kx 112 log (x+) has one soluhion

A: Just use basics of logarithm.

Q: a and In 3 = b. Use properties of logarith 31. In 1.5 %3D In

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: Select all that apply: log4 (114) = 11 4log,(11) = 11 O 4log11(11) = 11 O log, (4") = 11 11log,(4) =…

A: Please refer the attached image for complete solution.

Q: Verify the following calculations: V3.1415(to.0011)=1.77243(to.00031)…

A: Given,  there are some equations, we have to verify it.

Q: 27a b² Evaluate log, (- V81cd whenever log, (a) = 4, log3 (b) = 0, log, (c) = -1, and %| log3 (d) =…

A:

Q: 8. If l is the output for Carmichael's function machine shown at right, how can you determine what…

A: Since the output for Carmichael's function machine is 1. Equate x2+2x+1 to the output value of 1 and…

Q: 8. Prove the following statements. (1) loga = 2 log, r (2) log VI = - log, r (3) log,4 r = log, Vr…

A:

Q: Express the following in terms of x without logs or natural logs 1) log100x 2) 1000logx 3)…

A:

Q: Compute 3 In(e) +2 log(10) 7 11 1 9. 3. B8

A: Solve by properties of logarithm.

Q: 16 of 25 Condense to a single logarithm. 3 log 8 (m) – 2log 8(4n) – 3log 8 (5k) Vm log (4n)² (5k)³ 3…

A:

Q: 12) eiven AMUEÍVRTAMA, S C«) X22x<0 2x+1, 0<xL2 a) Evaluate f at x = -1,0, and 5. If not defined,…

A:

Q: Find the least integer n such that f(x) is O(x") for the function 3x +x log ax

A: This is a problem of finite math, and complexity.

Q: - 4 ) if f(x)= log3 3-2 (x3 – 4) (x3 – 2)In(3) 6x? %3D (..3 ..3

A:

Q: Prove that log3(25) is irrational.

A:

Q: We conclude that: for every additional distress input, the brain activity increases by 0.061 units…

A: Answer:----.               Date:----6/10/2021 since slope is change in dependent variable with 1…

Q: why the discrete log problem mod p = 100000005821 is especially insecure.

A: first  of all we must know about the discrete log problem.if G is multiplicative cyclic group and g…

Q: Employ Stirling's formula to compute y122 from the following table = 1 + log 10 sin x) : 10 11 12 13…

A:

Q: Which of the followingis the domain of the function m(x)=log12(|15-24x|)? @ dom m: {x|x€R,x

A: