The derivative of log, () is Recall that log, (x) = In(x), and that In(e) = 1. Putting these facts a In(b) together, we see that: 1 the derivative of In(x) is -. That is to say, the natural logarithm function, In(x), is the one whose derivative formula is simplest. (This is a big reason why it is used in mathematics instead of a logarithm with a more "psychologically comfortable" base, like base 10.) For the function f(x) = 10 ln(x): f'(x) = f'(2) -

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

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Q: 1. Consider the function g(x) = -2((x + 4))³-5 3 (a) What is the base/parent function? (b) Describe…

A: We have to find parent function for the given function.

Q: which of the following expressions is equivalent to: 3cot^2(t)/csc(t)   a. 3-3cos^2(t)/cos(t) b.…

A: This question is related to trignometry, We will solve it using trignometric identities.

Q: One of the following is False:

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Q: The domain of the logarithmic functiort f(x)=log_(a)x is

A: We find domain of the logarithmic function f(x)= logax.   Where, a > 0 is a constant.

Q: 1. What is log,, 100? What about log,00 10? 2. What is log, 4? What about log, 2? 3. Express b as a…

A: values=?

Q: The value of x for: log, (e) +4u) =x'log(10) is: %3D

A: Given equation is : logee+4-2log4x=x-1log102 To find the value of x. Use the property of logarithm ,…

Q: 1) (20 pts) If log, = X, express log, in terms of x 2) (40 pts) Simplify and find the value of 1 1 1…

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Q: ) f(x)= 3x 10 4

A: Solution- f(x) =3x4    we can write f(x) =y    To calculate inverse function, replace x and…

Q: 2) If x=0 and y=5 Check if the following statement is true. Explain and show your work. log, (5x –…

A: log of negative number does not exist

Q: 9.1) How would you compute log(4531.2) using a table with inputs between 1 and 10? Can you explain…

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Q: Given that log,(N)=2, then logl- O-1

A: We can use the concept of logarithm in order to get the solution.

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: Let b be a real number. By considering properties of exponential functions, show that the points…

A: We know, for any real number b > 1,         b0 = 1      => logb(b0) = logb(1)       =>…

Q: 3. Express as a single logarithm: 3 log 2 + log x - log (4x) log(8x) A. log(4x) В. log (2) C. log…

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Q: (a) If log, a = p and c=a², find, in terms of p, (i) log, c (ii) log, b (b) Given that log, a = 2…

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Q: Examine the change of the function and draw its graph: 2x-1 y =

A: Given: The function in x is given,           y=2x-1x3ex-1x Objective is to find the change of…

Q: If log, æ = 0.63, log, y = 1.46, and log, z = 1.77, loga

A: As we know that, The logarithmic properties: 1). logaxb=b·logax 2). logaxy=logax+logay 2).…

Q: 1. Use the definition of the logarithmic function to find x in the following equations: a) log, 25 =…

A: NOTE:- As Posted multiple independent questions,we are answering only first question as per bartleby…

Q: Evaluate the following logarithm expressions to verify the change of base rule. la. log:(50) = (use…

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Q: 17. Given y = -log3 (81(x - 2)²) a) Rewrite using the laws of logarithms.

A: The objective of the question is rewrite the logarithmic function.

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: