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

Q: 8) Using Theorem 6.2, show all work and determine the smallest integern for which f(x) = 2x3 +…

A:

Q: Assume that for some base a, logąx = 0.3000, logay = 2.8642, and logąz = 1.7642. Find %3D %3D loga…

A: log (mn)= log(m)+log(n)logmn=log(m)-log(n)logam=m log (a)

Q: 9. What is the maximum value of |Log z| |2| 1? on

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Q: .Expand log (1 + sin x) in powers of z as far as the term in r.

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Q: Find the greatest integer less than or equal to log29 S2²10 log₂ (x³ + 1) dx + S₁ 3 (2-1) dx.

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

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

A: Given

Q: Given that log4(y-1)+log4(x/2)=z and log2(y+1)+log2x=z-1, Show that y2=1+8z and find the possible…

A: Concept: Logarithm base change rule: logb(x) = logc(x)  logc(b) Logarithm quotient rule: logbxy=…

Q: The value of c which satisfy the conclusion of Rolle's Theorem for f)= log(x²+1)-log(2) on [-1,1]is:…

A:

Q: 6. Use rules of logs to write as the log of a single quantity. a) 2log3 x - log3 4 b) In x + In(x+1)

A: We will use the listed properties of logarithm to solve this question.

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: - Express as a single log. 3 log4 x + 2 log4. log4 y - Show your work

A:

Q: Express as a single logarithm   In x2 -2x-24/x-2-In X2 +2x-8/x+9 + In(X2 -12x+36),  x>0

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Q: Prove that Log(2) is discontinuous on R, the nonpositive real axis.

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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: 1. The solution to the cquation 53x = correct order on the right of the question. 4x+1 is given…

A: Re arranging steps in correct order,..

Q: The graph of every exponential function f(x) = ax , where a > 0 and a ≠ 1, passes through three…

A: f(x)=ax

Q: (3) Find the domain of f(x) = log(6 + x – x²) (A) (-∞, 3) (B) (-2, 3) (C) (3, ∞) (D) (-∞, -2) U (3,…

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Q: Express as a single logarithm   In x2 -2x-24/x-2-In X2 +2x-8/x+9+ In(X2 -12x+36),  x>0

A:

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

A: To Discuss: a. Does fx=logarithm x, with base 12 approaches a certain real as xincrease positively?…

Q: 3) In x-log x = 1. Answer should be in the natural exponential form. %3D

A: This is complicated and lengthy problem, so I can do it in Advanced Mathematics.

Q: a) In (x – 7) = 6 (b) In (x + 9) + In (x- 9) = 1 (c) log sx - log 52x = 2

A:

Q: Solve the following d. In 3- Inx - In (x + 5) = 0 e. Log4 (x+ 2)- log4 (x - 1) = 1 f. Log2 (x-1) –…

A: The detailed solution is as follows below:

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

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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: For which value(s) of k, if any, is the function 1 (²) = x [kx² - log₂ (x) 2xk²x + 5 continuous on…

A: Use continuity definition of function

Q: How large does x have to be, so that e^(-x/10)<0.1?

A: We need to find the values of x for which the following inequality holds good.

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

A: Just use basics of logarithm.

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: 5x + 2 lim log + 6 10x + 12 ° X-

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Q: - f(x) = - f(x) = x-2 g(x) = 5 In x - 2* g(x) = 4x' log, x %3D f(x) = 10* · e*

A: Solution of question is written in below steps.

Q: What transformations would map the graph of f (x) = log3 (a) onto the graph of g(x) = log3 (81z³)?

A: Given data fx=log3x gx=log381x3

Q: Suppose that log3(x) = 5.3 and log3(y) = 2.1. Evaluate the following exactly, and show your work a.…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 2. What is the extraneous root of 2 log3(x + 4) - log3(-x) = 2?

A:

Q: Evaluate y for the fx)= 4"-5 log,(x) 4*ln 4- Inx 4- x In 9 4- In 9 4'ln 4- x In 9

A: Answer

Q: 2. Show that x– log (1 +x) < く 2 (1+x) ' ザ-1<x<0.

A:

Q: 2 log(x+y) = 3log3 +logx + logy

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Q: Given that log2=x, log3=y, and log7=z, express log15 in terms of x, y, and z.

A: Given that, log2=x,  log3=y,log7=z The objective is to express log15 in terms of x, y, and z.

Q: State the restriction(s) on the variable x in log(2x-5) – log (4 - x)

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Q: Find the domain of each fucntion: a.) f(x) = ln(2-x) b.) f(x) = log2(2x-3))

A: Calculation:Note that the argument of the logarithm function always positivea.) The domain of the…

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

A:

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

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Q: 12) eiven AMUEÍVRTAMA, S C«) X22x<0 2x+1, 0<xL2 a) Evaluate f at x = -1,0, and 5. If not defined,…

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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: - 4 ) if f(x)= log3 3-2 (x3 – 4) (x3 – 2)In(3) 6x? %3D (..3 ..3

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Q: Prove that log3(25) is irrational.

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Q: Evaluate So ·∙log 1+ax 1-ax (: ( dx x√√1-x²

A: A very good problem. This problem illustrates the power of differentiating under the integral sign.…

Q: why the discrete log problem mod p = 100000005821 is especially insecure.

A: first  of all we must know about the discrete log problem.if G is multiplicative cyclic group and g…

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.