15. Given prime p := 8901577, primitive root g := 353, y := 7321, solve the follwoing Discrete Logarithm Problem via Pohlig- Hellman algorithm:

Q: 1- Evaluate without a calculator. Show your work. a) Log 0.000001 b) log4 (1/16)* 33 51/4

A: The given problem is to evaluate the given logarithmic terms. Given logarithmic terms Log(0.000001)…

Q: Deduce that log (1 + x) 0. If fix) = log (1 + x), x > 0, uning Maclaurin's theorem, show that for…

A: Given that: fx=log1+x, x>0 To show  log1+x=x−x22+x331+θx3 for 0<θ<1 and log1+x<x−x22+x33…

Q: in a reaction time task, your reation time was 250ms when 2 choices were given in a task. when there…

A: The main objective is to find reaction time, if 8 choices were given in the same kind of task.

Q: 2) Solve log 48 = log (x + 7) + log (x - 1) Be sure to verify solutions and show if there are any…

A:

Q: The graph of y = log6(216x) can be obtained by stretching or translating the graph of y = log6x. A)…

A:

Q: a) Use the Laws of logarithms to rewrite the expression log in a form with no logarithm of a…

A: Use laws of logarithms to rewrite the given expressions in expanded form and single log.

Q: 7. Solve the following. Check for extraneous roots. a) log₂ (x + 25) − log₂ (x - 1) = 3 b) log x +…

A:

Q: Q3 Identify the restrictions on x and solve for x. log,(6-x) = 2 0 < x < 6, x = 4 0 < x < 2, x=2

A: Identify the restrictions on x and solve for x  logx6-x=2

Q: Expand the following: a) log 3x2/ y4 b) log5 x5 (square root of y)/ z3

A:

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: 24) Use the Laws of Logarithms to combine the following expressions. a) log,(x – 2) + 2log2(x)…

A:

Q: 7. 8. Another way of writing 5 = log41024 is a) 54 = 1024 Evaluate log525². a) 25 b) 1024 = 45 b) 4…

A: logbx = y is equivalent to by = x ,where x &gt; 0 ,y &gt; 0 ,b &gt; 0 ,b ≠ 1.logaa = 1 for a&gt;…

Q: Prove that (ij) d dx² (log √√g).

A:

Q: 3. Evaluate: a) log₂ 16 = b) log: 100 c) log, 3= d) log₂ √8= ask yourself, "what exponent would I…

A: As per Bartleby rules we have to answer only first three questions.

Q: 8) Solve for x when log10¹ = x a) log 8 100,000,000 b) log 10 c) 8 d)

A:

Q: 3 = log,√7 = Log₁4/7=

A: a) lne53 b) log77 c) log774

Q: Estimate log(58607) by deciding which two integers it is between: __

A: Using the following result, we could estimate the log value given in the question. logbbm=m; here…

Q: 9) Write log 40-log 10- log 2 as a single logarithm a) log 2 b) log 8 m c) log 20 d) log 32

A: log(m) - log(n) = log(m/n)

Q: logi2144

A: Here, we need to simplify log12144. So,               log12144Factor the number:…