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

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: 11. log( 2x + 9) + log( x + 3) = log( x² +1) Solve.

A: Logarithm is the inverse function to exponentiation. Logarithm of a number is the a quantity…

Q: For all values of x > 4, log (x + 4) + log (æ – 4) = log (2x) True False

A: logx+4+logx-4=log2x

Q: Find the dom ain of defination of each of the following functions: f(x)=log{1- log,,(x² - 5x +16)}.

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Q: In(t+7)=-1 in exponential form

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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>0 To show  log1+x=x−x22+x331+θx3 for 0<θ<1 and log1+x<x−x22+x33…

Q: Find Satisfying log 10916 the Smallest Integer the X -1 equation +2= log, x-3 ㅗ 6

A: given equation

Q: 3x (37) 2y (d) In (e) log₂ (x³) (f) In (2x³e4)

A: Expanding given terms.

Q: olve for x

A: Given,       log3x2-3x+5

Q: h(x) = log3(x − 3) + 2 what is the x-intercept

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: 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) c)…

A: We  have to calculate this equation by means of logarithm.Note: According to the guidelines we are…

Q: T(X) = 4 +

A: We have to find

Q: 4. Solve for x log (35-x³) log (5-x) = 3

A: Given log35-x3log5-x = 3

Q: f(x) − log2(1 - 3x)

A:

Q: If log(x + 13) + log(x – 13) = The value of æ is

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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: Suppose the functions f, g, h, r and I are defined as follows: f (x) = log+log x 3 g(x) √(x+3)² h(x)…

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Q: Q4B- Write user define- function program to find 3 1 ((x - 1) 1 ((x-1)) (x - 1) (x + 1) 3(x+1) + - +…

A: Here we write a python code to define the user define function.

Q: 3. 9. a) Solve for x: log4 xX = b Write as a single log: 2log, 3x + 3log5y – 4log5z

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Q: In 2 log2x

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

Q: A3. (a) (i) Express 2ln x – ln √x as a single log in its simplest form.[

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Q: Solve for x, log 7 (x − 4) + log 7 (x + 2) =1 and state restrictions

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Q: 16. Solve. a) log (²x) = Text 2 b) log4(x²7x − 18) - log4(x + 2) = 3

A: a) log3⁡(2xx−7)=2

Q: State the domain and the range of f(x) = log10 (-4(x - 12)) +5 Domain:{ ER 3}, Range: {y < R}…

A:

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.