Let (2) denote the branch of the logarithm defined on C- [0, ∞) with 0 < Im(l(z)) < 2π. For the branch of zi+3 derived from 1(z), find (-i)i+3.

Q: Let f(x) = log₂ (x²+2x+1) and g(z) = log₂(x+1), find h(x) = f(x) + g(x). Oa) h(z) = 0 Ob) h(t) = 2 O…

A: This question can be solved using the concept of logarithmic function.

Q: For any real number b > 1, and any real numbers x True False log, (x - y) = > 0 and y> 0, it must be…

A:

Q: State whether the following statement is true or false. The domain of f(x)=loga x, a>0, and a ≠ 1 is…

A: A logarithmic function  f(x)=loga x,  where x&gt;0 is equivalent to x=ay , where x &gt;0.  Its…

Q: for: Q1) Find dx 1) y = log3(3x³ +x²)² x In(sec-1 /ã)

A: I have solved question 1 for next question repost.

Q: X* Q: Prove that the function y- 2 2 x+1+/log Vx+Jx +1 + log satisfies the relationship 2y=x dx

A:

Q: f(x)=√ g(x) = log(10²tan¯¹(x), h(x) = x 2) Sketch the graph of g¯¹(x), 4)Find [g¹(x)].

A:

Q: a) x1+2log x = 100.x log x

A: Since you have asked multiple questions in a single request so we will be answering only first…

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: Evaluate (a) log(2-j3)(6(sin(√ī})² (b) 11/2

A: Given:  log2-j36sinj2 jjj2 To find: We have to evaluate the given expressions.

Q: Find the equation of the vertical asymptote f(x) = log(x – 1)

A:

Q: (9) Express the domain of f(x) = log(2x - 4) in interval notation. A (0,2) B (-2,00) C (2,00) D…

A:

Q: Find the domain of the function of 5 log₂ (4-x²)+11 f(x) = 12x-31-2 + sin¯¹(1 − 2x) Express your…

A:

Q: Let ƒ(x) = log₂(x + 1) and g(x) = log₂ (z − 1). Find h(x) = f(x) + g(x). - O a) h(z) = log₂ (21) Ob)…

A: This question is related to Functions, we will solve it using given information.

Q: 19) Consider the function y = 5 log (z + 12) – 8. Complete the sentence about the graph of the…

A: Given that  Function y = 5log(x+12)-8

Q: 3) Calculate by means of the logarithm: a) x¹+2log x= 100.x log x b) log(x+2)+log(x-7) = 2.log (x-4)…

A:

Q: Let f R*R, defined by f(x) = 3*, then f(x) = %3D O log,3 3* o log3x log3

A: See solution below.

Q: Prove that the inverse hyperbolic function can be written in terms of logarithms: cosh¹x =…

A: We have to prove that cosh-1x=lnx+x2-1 for x≥1.

Q: Show that the function is continuous. f(x) = log2(x2 + 1)

A: Consider function  fx=log2x2+1   x fx -4 4.087 -3 3.322 -2 2.322 -1 1 0 0 1 1 2…

Q: dy Q1) Find dx for : 1) y = log3(3x3 + x2)2 x In(sec- x)

A: I supposed to do only first question as our company guideline. Please repost other question as next…

Q: Let f(n) and g(n) be asymptotically positive functions. Prove the following conjecture: f(n) =…

A: We will use the concept of limits to prove the given conjecture.

Q: 7. Given the functions f(x) = log₂ (x-1) and g(x) = log₂ (9-x²), c) Determine (f-g)(x). b) State the…

A:

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

A:

Q: Express the function h(x) = 5log(x² + 6) the form fog. If f(x) = 5log(x), find the function g(x)

A: We can find the function g(x) from the given composite function in the below steps.

Q: 1 f(t) = log13 (t) and g(t) t - 9

A:

Q: The function f(x) interval [1, e] at x = Hora lo 0 x is the nat

A: