Without using log tables prove that 1orsid ei boeu ss to 16 +12 log10 15 25 +7 log10 24 81 = 1 80 log 10 2+16 log10 -

Q: If w=log(ysinx+xsiny) then prove that wxy=wyx

A: If w=log(ysinx+xsiny) then prove that wxy=wyx

Q: PROVE that log, 100 = 2(1 +log; 2)

A: We have to prove that                                     log5100=21+log52

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

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Q: Express the indicated logarithm in terms of ?, ? and ? with the assumptions that log 2 = ?, log 3 =…

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Q: log5 6 is irrational

A: We can prove given result by contradiction method:

Q: Show that |Log(2)| < | In |2|| + T.

A:

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&gt;0 To show  log1+x=x−x22+x331+θx3 for 0&lt;θ&lt;1 and log1+x&lt;x−x22+x33…

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: 1-In (-) + In(2x) = In3 2- 4 log 2 - log3 + log16 = x 3-Expand In [x? sin x /Vx2 +1]

A: To find the value of x

Q: Show that 3x2 + log2x2 is Theta(x2). log2x is log base 2 of x.

A: Consider 3x2+log2x2 . It is known that  log2x2&lt;x2, for all x&gt;0. Then, log2x2&lt;3x2 for all…

Q: The union of left ray topo log y and right ray top log y on real numbers is usual topo log y True…

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Q: Hiw/ prove That: logit 210gi @ log (iti)= 2 log (iti) ® log é#2log Z it z=

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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: PROVE that log5 100 = 2(1 + log5 2)

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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: 2 1. Express log,(64 x v64*) + log, (46 V256. 43 logarithm

A: Using log44 = 1

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

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Q: write as sum/difference of logathirims. express powers as factors.    log2 (xy^6 / z^2)…

A: Logarithm

Q: Suppose that a and y are real numbers such that log2 (x) = – 3 and log2 (y) 6. Calculate the…

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Q: Which of these are equivalent to log(5r)+ log(3x)? Select all that apply. O log(15z) O log (152*) O…

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Q: One of the following is False: Select one: Log(z12) = Log(z11) + Log(z2). %3D dogz = z if z 0. %3D…

A: Given :- find the false statement.

Q: Show that log,(n) € O(log,(n)) for any b>0 with b 1· Generalize this result.

A:

Q: Use a graphing utility to evaluate the logarithm by the methods given below. (Round yol In(29) (a)…

A: Answer

Q: In LRT reject H, when Ais small, so we reject H, when the value -2 log A is small Select one: True…

A: Answer : False

Q: In LRT reject H, when Ais small, so we reject Ho when the value -2 log A is small Select one: True…

A: Answer : False

Q: What will the coefficient (x – 1)² in the expansion of loge x about x = 1 ? %3D

A: Introduction :

Q: Solve the following d. In 3- Inx - In (x + 5) = 0 e. Log4 (x+ 2)- log4 (x - 1) = 1 f. Log2 (x-1) –…

A: The detailed solution is as follows below:

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: 4. (a) Use logarithm properties to expand In ( (@+5)(x – 6)² (x+ 3)3). (b) Rewrite log3(x) + log3 (y…

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

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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: 9.5. Show that (a). Log(1+ i)? = 2L0((1 + i) but (b). Log(-1+i)² + 2Log(-1+ i). %3D

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: . if võ =o, i =1 and Ju = 2 estimate 13 %3D by constructing Logrange polynamial, Itn with the exact…

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Q: If n is a power of 2, prove that M(n) = (n log n) / 2 , using Master of Theorem method. Show all…

A: Given:n is a power of 2To prove:M(n)=(nlogn)2using Master of Theorem method.Proof:Inorder to prove…

Q: 13. Determine whether or not each statement is true or false for all x>0 & y> 0; If a statement is…

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Q: 6) Given that x = log, b. write down an %3D expression for b in terms of a and x. log, t that log, t…

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Q: 5. Prove that if {a,}f° converges to 1, then {an}° converges to 1. Hint: You may use a logarithm…

A: If an1∞ converges to 1, then an1/21∞ converges to 1.

Q: Which of the following are equivalent to 5 · log (u-1/6)? Assume u > 0. 1 O log log (u/") 1 log (u")…

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Q: Solve the following d. In 3- Inx - In (x + 5) = 0 Log4 (x + 2) – log4 (x - 1) = 1 e. f. Log2 (x-1) –…

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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…

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

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Q: Show that 2 + 11n² log,(n³) – 7 = 0(n³)

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Q: Prove that log3(25) is irrational.

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Q: Prove the following equation(with appropiate restrictions on the variables) logx–2=log(x/e²)

A: Here we will use the following formulas logab = log a -log blog(ax) = x log alog e = 1 Consider…

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: V (P) = log (2) (5) + + log (4) 2, + log (8) = log (4) + ...

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Q: Show beta (a,b) belongs to the z- parameter exponential family.

A: