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

Q: By using u=ln(3x) and dv=6x dx, find ∫ 6x ln(3x) dx. Be sure to include the argument of the…

A: Consider the integral

Q: (ii).Given that log, (y-1)+log, = z and log, (y+1)+log, x= z – 1, Show that y = 1+8° and find the…

A: Given: log4y-1+log4x2=zlog2y+1-log2x=z-1 . . . . . (equation 2) Concept: Here we shall use the…

Q: Given that 4.0 4.2 4.4 4.6 4.8 5.0 5.2 y 1-3863 1-4351 1.4816 1-5261 1.5686 1.6094 1.6487 5-2 3…

A:

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

A:

Q: Evaluate in terms of gamma function: e- ydy

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: 8. Given that (2x-x*); 0<x<2, S(x) = ; elsewhere. a) Calculate E(X), E(X²) and E 2- X

A:

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: Given that log 2 = x, log 3 = y and        log 7= z, express the following expression in terms of x,…

A: We will write 0.3 as fraction. That is 3/10

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

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: If log, (8) z 0.7 and log, (7) z 0.6, find the approximation of log,(448) =

A: Follow the procedure given below.

Q: Given that log, X = 3, log, Y = -1, and log, Z = 2, %3| evaluate log, X²Y Z

A: NOTE: Refresh your page if you can't see any equations. . here we have

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: Suppose the functions f, g, h, r and are defined as follows: 1 1(x) = 1093 / +10g, x log3 g(x) =…

A:

Q: Let f(x,0) e*(1 – 0)"¯, then the exponential form for this pdf can be written as expin)-x innti - 6)…

A: The given statement is false. Therefore the second option is correct.

Q: 3. Given that log,x = 2 and that log, y = 3, use the logarithm laws to expand the following and…

A: \Logarithm rules:logaxy=logax+logaylogaxy=logax -loga yloga x4 =y loga xlogaa =1

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: 24. For which b does the definition of log,x just given make sense, and why? Is this the same…

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: Prove Equationally that A → BF¬B → ¬A.

A: let us check whether the given statement is true or not

Q: At what value(s) of x does e^(-x2) =x2 - x + 1?

A: To determine the values of x at which,

Q: 4. What is b if (log, x)' :? Зх

A:

Q: Given z=(3+2i), solve e^logz

A:

Q: Evaluate loge 7 by Simpson's (i) rd, and (ii) th rules.

A:

Q: 4 Given that log m3 ~ 0.945, log m4≈ 1.192, and log m7≈ 1.674, find log mm log m (Type an integer or…

A:

Q: 5) Show the proof that loga M" = r· loga M

A:

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

A:

Q: If H(x) = log, 1/x, show that H(blz) = 1/z.

A:

Q: For Problems 9 and 10, prove or disprove the following. 9. ez = ez 10. Ln z = In Z

A:

Q: Solve for A: AR+AT=E

A:

Q: Given that x, y, z >1 and w be a positive number such that log, w = 24, log, w = 40 and logrvz W =…

A:

Q: -Given that p log, 5, q log, 2 express the following in terms of p and/or q. log, 0.625

A:

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: Given that log z =2, log y = 3 and log z = 4 find log () %3D O 13 O 9 8. O 7 O 11

A: We are asked to find the log

Q: Let I be ar. V. has a Binomial dist. B(n,@) with the Pid.f. fex; G)o-0^,X:o,n Show that fex;)…

A: Given that X is a random variable which has binomial distribution Bn,θ with p.d.f is given by:…

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: 3 Given that xand y are real numbers, x>0, if 4"-3x' 16, log, x=, r+1 y find the value of x

A: Given: x and y are two real numbers, x&gt;0 4x-3xy=16 log2x=x+1y We can write, 4x=16 +3xy⇒2x2=16…

Q: 10. Use Figure 6 to find a value of 8 > 0 such that the following statement 1 1 <e for e = 4 holds:…

A: Given that,

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

A:

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

A:

Q: b) Given that log, (y-1)+log,|| |= z and log, (y+1)+log, x = z-1, Show that y? =1+8² and find the…

A:

Q: If we know that E (") (x" 1) = ("†").t then show that Eo (") -C") r3D0

A: Given information: The given theorem is:

Q: show that for positive epsilon, |x-4| |3x-12|<e

A: a⇔b implies if a holds then also b holds and vice versa.

Q: Find of, af , for f(x, y) = log₂ (3г² - +y)

A: Solution of given question is written in below steps.

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

A:

Q: Given that log z = 2, log y= 3 and log z = 4 find log () %3D %3D %3D O 29 O 25 O 31 O 26 O 27

A:

Q: find the general for al soluh'an 3yC3) (e)

A: The given differential equation, y(4)+3y(3)+3y(2)+y'=0

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.