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

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

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

Q: Find the greatest integer less than or equal to log29 S2²10 log₂ (x³ + 1) dx + S₁ 3 (2-1) dx.

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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.

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Q: Find the inverse 2-Transforrm of log(z f log 241 by Power senies method and by division method

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Q: 6. Use rules of logs to write as the log of a single quantity. a) 2log3 x - log3 4 b) In x + In(x+1)

A: We will use the listed properties of logarithm to solve this question.

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: 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: Evaluate the expressio 1 log 6 6 1 log 6 6 %3D

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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: Prove that Log(2) is discontinuous on R, the nonpositive real axis.

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

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Q: then A-wL Show that Ucri@) = Lojr Where the natural Log 1S USed is harmonic then find a harmonic…

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Q: Q4. Find the real root using Regula Falsi method correct to 3 decimal places of the following x…

A: f(x)=x log₁₀ x -1.2 f(0)=0-1.2=-1.2 f(1)=1 log₁₀1-1.2=-1.2 (-ve) f(2)= 2 log₁₀2-1.2=-0.59794 (-ve)…

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

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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: 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: Use the properties of logs to expand: x+5 b) log+ 3x-2 d) log, x(x + 4)

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

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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: Find a real root of 3x – log10 x – 8 using the Successive Approximation method. Correct to four…

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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: 10. Express 17* as a power with a base of 2. log2 log 17 b. 2 4 log 17 log2 d. 2 a. log, 17* c. log,…

A: As we know from the logarithmic property; logaxb=b·logax, where x,a&gt;0 &amp; a≠1   Let, 174=2x…

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: Find the smallest positive integer n so that f(x) = x8-log(x³ ) + x6-log(x5) is big-O of xr.

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Q: (2) Combine the following into one single logarithm with a coefficient of 1 in front of the entire…

A: 6log4x-5-34logx+log9x-1

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: 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: Hiw/ prove That: O logi+ 2logi

A: The complex logarithmic function is defined as: log z=ln|z|+i·Arg(z) Where |z| represents the module…

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: In arcsin x (V1-x²)arcsin x

A: Given:     ∫lnarcsinx1-x2arcsinxdx    =∫lnarcsinx1-x2arcsinxdx substitute…

Q: Suppose that log3(x) = 5.3 and log3(y) = 2.1. Evaluate the following exactly, and show your work a.…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 4- If X is an exponential with parameter 1, then 2X is chi-square with 2 degrees of freedom. O True…

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

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Q: Evaluate y for the fx)= 4"-5 log,(x) 4*ln 4- Inx 4- x In 9 4- In 9 4'ln 4- x In 9

A: Answer

Q: 2 log(x+y) = 3log3 +logx + logy

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Q: Find the greatest integer less than or equal to log29 S² log2 (x³ + 1) dx + (2x - 1)³ dx.

A: At first, we have to evaluate: I=∫12log2x3+1dx + ∫1log29(2x-1)13dx

Q: Prove that| log,x E O(log2 x)

A: We know the relation |_log2x_|≤log2x≤ log2x. That is the floor value of any real number is less than…

Q: Without using log tables prove that 1orsid ei boeu ss to 16 +12 log10 15 25 +7 log10 24 81 = 1 80…

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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: Prove 42 tan xdx =1-log 2 3

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Q: Prove that log3(25) is irrational.

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Q: Evaluate So ·∙log 1+ax 1-ax (: ( dx x√√1-x²

A: A very good problem. This problem illustrates the power of differentiating under the integral sign.…

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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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.