(b) Show that u(#) = log log (1 + l#|") belongs to W(U) but does not belong to L(U).

Q: The logarithmic function f1x2  ln1x  12 has theasymptote x

A: Given f(x)=ln(x-1)

Q: a- Simply the following 1 1. Inx – In(x2 – 1) + 2ln(x + 3) - 2. 5log2 + log3 – log8 b- find x for…

A:

Q: Prove that In x lim I xP for any number p > 0. This shows that the logarithmic function approaches o…

A: Given

Q: Show that S log(sin x) dx = -log 2.

A: To show that ∫01logsinπxdx=-log2 using the given figure.

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: If x2 + y2 = 25xy . Then prove that 2 log(x+y) = 3log3 +logx + logy

A: It is given that x2+y2=25xy add 2xy to both sides  x2+y2+2xy=25xy+2xy using the formula…

Q: Differentiate the following functions: 1. y = tan(log25x) + x. log3(sec x) 2. logyx = logxy %3D

A: We havey=tanlog2 5x +x.log3 (sec x)Let  u=tanlog2 5x     and    v=x.log3 (sec x)Now y=u+vdiff.…

Q: 1. Show that (a) Log(-ei) = 1 - ži;

A:

Q: 2. Differentiate: a) y = log2(3x) %3D 2 b) f(x) = –7 log(x²) %3D

A:

Q: 10) Solve the logarithmic equation In(x+1) – In(x – 4) = 1. -

A:

Q: 4. Differentiate the function. f(x) = log3 (x In x)

A:

Q: Does the function f(x)= logarithm x with the base of 1/2 approach a certain real number as the value…

A: Given

Q: 9. Condense (log4x – log4y)+2 log4(x+1) into a single logarithm with a coefficient of one.

A: Explanation of the answer is as follows

Q: How is the graph of y =log(x) transform to produce the graph of y=log(2x)+3

A: Given graph of y = log(x), transform it to get the graph for y = log(2x) + 3.Let us first discuss…

Q: at any point h (1, 1) is logx – x

A:

Q: 4. The domain of the logarithmic function f(x) = log, x is

A: fx=logax

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

A: It is obvious that log2x≤log2x so, log2x∈Olog2x.

Q: 54. For any positive constant k, the derivative of In (kx) is 1/x. Prove this fact (a) by using the…

A: Given for any positive constant k, the derivative of ln (kx) is 1/x. To prove that  a) by using the…

Q: write the logarithmic equations in exponential form.

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

Q: 2. Express as a single logarithm 4 log, x² + 3 log, ) – log, x X 5

A:

Q: 14. Find the domain of definition of the function 31 Vx + 5 X-5 y = log10 (,2 x² – 10x +24

A: The domain of a function is the set of input or argument values for which the function is real and…

Q: 2. If the rate of transmission of an additional case of covid-19 is 0.3 per day starting February…

A:

Q: 4. Show that id 5D accuracy is required to calculate the value of log(1+x) at x=0.1,0.5 by using the…

A: Given equation is log1+x=x-12x2+13x3+.....+-1n+1nxn+Rn+! So, Rn+1=-1n+2n+1xn+1 So, maximum relative…

Q: 1. In 2x - 21n/2y³ + In(xy)² as a single logarithm.

A: since you have posted multiple question i can do first question as per pur company guidelines please…

Q: dx Evaluate log - 1+ax 1-ах

A:

Q: Does the function f(x)- logarithm of x with the base of 4 approach a certain real number as the…

A: Consider the given function as fx=log4x.

Q: Solve for x. (a) In (x – 3) = 7 (b) In (x + 4) + In (x - 4) = 1 (c) log gx² - log ,2x = 3

A:

Q: Combine into a single logarithm. In(x – y) – 2 In(x² + y²) OIn (x-y)3 In (x²+y²)* In Va-y) (x²–y²)?…

A:

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

A:

Q: Evaluate log2(x²) dx In(2) -log2(x²) + C 4 In(2) log2(x²) + C n(2) (log.(r2))2 (log. (x2))2 1r 4…

A:

Q: - If y=a² 1-log.x and z=a* 1-log, y , then x is equal to

A: Introduction :

Q: 4. The expression log(sinx) – log(cos.x) , 0<x<, is equal to A. log(sin x cos x)

A:

Q: Find all x- and y-intercepts of graph of y = -3 +log2(x2 - x +2).

A: Given function is y=-3+log2x2-x+2

Q: Find all positive values of 'a' for which the equation log (ax) = 2 log (x + 1) has the unique root.

A:

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

A: Just use basics of logarithm.

Q: 7. Use properties of logarithm to expand In (y³z²Vx – 1)

A: Property of logarithm

Q: 7. Differentiate y = log10 (x² + 1)² b. 4xlog10e x²+1 a. 4x(x² + 1) c. log e(x) (x² + 1) d. 2x(x² +…

A:

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

A:

Q: Determine the maximum and minimum values of the function f(x)=-4 •log 2x on the interval [1,4]

A: Given function is  on interval [1, 4].

Q: (b) Show that 1 1+ 2 tanh- (2) = ; log

A:

Q: Suppose a certain population is initially absent from a certain area but begins migrating there at a…

A: Consider the provided question, Suppose a certain population is initially absent from a certain area…

Q: 6) If u = log (x² + y²), then prove that log (x² CSScanned with CamScanner dydx ôxôy

A:

Q: d Find (2"). Type In(x) for the natural logartihtm dx function.

A:

Q: 2. Evaluate [log(-1-/)(-2- j2)] tan(4 + 3i) cosh-1

A:

Q: Prove that A log ƒ (x).= log|1+A7®) f(x)

A:

Q: 3. Find syz for ys = In(x + yz) – xcoth- log ()-

A:

Q: What is the linear approximation of log base 5 x at x=5

A:

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…