101. Show that log,(x + V – 1) + log.(x - Vr - 1) = 0.

Q: 3. Find syz for ys = In(x + yz) – xcoth-1 log ().

A: Given : Let us consider the given value as,  ys=ln(x+yz)-xcoth-1logzy

Q: Use the trapezoidal rule with five function values, together with appropriate log laws, to show that…

A:

Q: Express In(1+r²) +In r- In sin r as a singel logarithm.

A: Use property of log :→n ln(m) = ln(mn)→ln(m) + ln(n) = ln(mn)→ln(m) - ln(n) = lnmn

Q: How do I expand this log expression? xz/5y x times the square root z over 5y

A: We have to expand the log expression:

Q: Show that for 2 degrees of freedom, the probability P of a value 1 of greater than yo is ex and…

A:

Q: 5. Show that --I+#^) log, (V +1- x) + log, (VF+1+x) = 0 x². x² + 1 + x

A: We know the property of logarithm, logb(a)+logb(c)=logb(ac)

Q: )For x>0, xER, find the 0() estimate of order of the function 6x* + 3x logx - 5x3 + 7x-9 *(x) = 3x3…

A: Given: 6x4+3x6logx-5x3+7x-93x3+2x2logx2-5x x>0, x∈ℝ

Q: 3. Use Log Rule to integrate. a. Sor5 Sdx а. бх-5 b. S; -dx x(lnx)²

A:

Q: Show that log, (Vx + Vx – 1) + log.(Vx – Vx – 1) = 0.

A: To show that logax+x-1+logax-x-1=0. Solution: We know that, logm+logn=logmn Simplifying the left…

Q: Which of the following functions grow faster than In x as xoo? Which grow at the same rate as In x?…

A:

Q: dy : Prove that dx or ỹ for expression y log2(x²) is equal to ỹ = 2[1-log2 x² In 2] %3| x2 x³ In 2

A: Given, y = log2x2x2    We have to prove dydx or y¯ = 21-log2x2.ln2x3ln2

Q: Order the functions f(x) = log2 x, g(x) = xx , h(x) = x2 , and k(x) = 2x from the one with the…

A: Consider the given functions fx=1og2x,gx=xx,gx=x2,k=2x.

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

A:

Q: Express log x Vy/z in terms of logarithms of x, y, and z.

A: Express log x4y2/z3 in terms of logarithms of x, y and z.

Q: 8. Let f(x) = log,(3x² – 2). For what value of b is f'(1) = 3?

A:

Q: Differentiate the function with respect to x f(x) = 2* · log37*²-4

A: If hx and gx are two differentiable function and fx=hxgx Then f'x=gx×ddxhx+hx×ddxgx

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

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

Q: Show that log, (x + Vx² – 1) + log,(x – Vx – 1) = 0.

A: Logarithm is inverse of exponentiations. A logarithm is easy method to express large number and to…

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: Show that J log(1 + tan0)d= log2

A: Given that: To prove:        ∫0π4log(1+tanθ)dθ=π4.log2

Q: 22. Suppose f(x) = log x + log(x – 3). Find the x-value for which f(x) = 1.

A:

Q: 64 J2C48=X Log,

A: Note :- As statement of problem missing we solve given problem for variable x  Given:- Log1/128…

Q: Find the exponential functions of the form f(x) ab* that pass througl

A:

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

A:

Q: 4. What is b if (log, x)' :? Зх

A:

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

A:

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

A:

Q: When comparing the f(x) = x² + 2x and g(x) = log(2x + 1), on which interval are both functions…

A: Let's find interval when both functions are negative.

Q: =) Express the new function h(x) log2 in terms of the original function f (x) log, (x).

A:

Q: Differentiate with respect to the independent variable: f(x)= log base 20 square root x

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: Which function rule should be used to transform any (x, y) point from f (z) log z to h (z) = -log…

A:

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

A:

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

A:

Q: 7. Find y'. y = log, (9– x-x)

A:

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

A:

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…

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: Find the least integer n such that f(x) is O(x") for the function 3x +x log ax

A: This is a problem of finite math, and complexity.

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

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

Q: Find for the following function: 3- y = log,(x - x) 4- y = In2

A: It is an important part of statistics . It is widely used .