30. log, (2) vs. log, (x) g(x) = log2(x)? Here is one way to find out. a. Use the equation log,b = (In b)/(In a) to express f(x) and g(x) in terms of natural logarithms. b. Graph f and g together. Comment on the behavior of f in relation to the signs and values of g. How does f(x) = log,(2) compare with

Q: 5. Find the equation of the line tangent to the graph of y = loge a when a = 36. 6. Show that there…

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Q: 6. The logarithmic function f(x) = In(x – 1) has the asymptote x %3D

A: Given, Logarithmic function, f(x)=ln(x-1)

Q: 6. Show that the principal branch of the log function can be described by the formula log(z) = S 1/w…

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Q: The effect on the graph of y = log,z if it is transformed to y = log,(z+3)? may be described as Oa…

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Q: - The property of logarithms states that log for positive real numbers b, x, and y, where b + 1.

A: According to the Quotient rule property of logarithm: logamn=logam-logan,    m,n,a>0 and a≠1

Q: 1. How does the graph of f (x) = log(10000x) compare with the graph of ƒ (x) = log x.

A: Solution

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A: By definition, The logarithmic function y=logax is defined to be equivalent to the exponential…

Q: 5) Sketch the graph of the following logarithmic functions by plotting points: a) f(x) = log5 x %3D…

A: given f(x)=log5x  and  g(x)=log15xwe have to sketch the given function by plotting points.   we know…

Q: 22. Express the signed area between the graph of y = - and the x-axis from x = 0.25 to x = 1 in…

A: Consider the given information. y=1x And, the given interval is 0.25,1. The area is defined as,…

Q: A logarithmic function, h, is plotted on the graph. h(x) 4- 2- -2 2 6 -2- 4- What is the approximate…

A: Approximate rate of change on the interval [-2,2]…

Q: A group of survivors on a supply run has returned to their base camp with a population of 2000. Two…

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

Q: 2. The function f(x) = log, x is the logarithm function %3D So f(9) = -- f()- with base %3D f(1) =…

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Q: When log y is graphed as a function of x, a straight line results. Graph the straight line given by…

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Q: Suppose f(x)=3•27x , find a constant b such that the graph of log b f has slope 1. b=?

A: Given

Q: (a) By drawing the graphs of the functions (x) = 1 + In(1 + x) and g(x) = V in a suitable viewing…

A: In the following diagram the logarithmic function starts out higher than the root function as…

Q: The logarithmic parent function y = log (x) has been transformed. What is the equation of the new…

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Q: Assume that your utility has a natural log function U(W)=ln(W), which is a concave function. Your…

A: Answer:----.               Date:----11/10/2021

Q: Disprove the statement log(x + y) = log x + log y by, a) Letting y equal a positive constant of your…

A: Given  The statement log(x + y) = log x + log y

Q: The graph of the function f(x)=log7(x) is stretched vertically by a factor of 4, shifted to the left…

A: Given: The given function is fx=log7x To find: Find the equation after fx is stretched vertically by…

Q: 1 1 1 The value of log, n log,n SI- log,™ -+- t.

A:

Q: 1. Find the function of the form y = log,(x) whose graph is given. y = y 1.5 (5, 1) 1.0 0.5 5 6 -0,5…

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Q: 17. What type of transformation would occur with the following logarithmic functions? f(x) = log,x…

A: Given that: f(x)=logbx& f(x)=logb(-x)

Q: 2. Determine if the function is an exponential function. f(z) = 2*

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Q: lot the graph for the following functions nclude at least two values between 0 <x < 1 1. f(x) =…

A: Given functions f(x) = log4x h(x) = log10x

Q: (9) Consider the graph of the function 1 f (z) = + In || (a) What is the domain of the above…

A: Since you have posted a question with multiple sub-parts, as per company guidlines we will solve…

Q: Can you show and explain properteis of the lognormal function: E(e^x) and Var(e^x)

A: Let us say X follow a normal distribution with probability distribution as shown…

Q: 5. Find the derivative of the following Natural Logarithm functions f(x) = In(3x – 4) a. b. 2

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Q: 54. For any positive constant k, the derivative of In (kx) is 1/x. Prove this fact (a) by using the…

A: Given for any positive constant k, the derivative of ln (kx) is 1/x. To prove that  a) by using the…

Q: Find the exact x-coordinate where there is a horizontal tangent line to the graph of f(x) = x8*.…

A: To find the exact x- coordinate.

Q: The function f1x2  log9 x is the logarithm functionwith base . So f192  ,f112  , fA19B  , f1812…

A: Given logarithm function is fx=log9x. We know that if logarithm function is logax then base is a.…

Q: Graph the given functions  f(x) =4^x    and   g(x) = log4X  on the same graph b)  Explain the…

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Q: Find the derivative f'(x) if f(x) = log 3x² A. (2/x) log 3x B. (2/x) log e C. (3/x) log 3x D. (3/x)…

A: Solution

Q: 1. If the logarithmic parent function, f(x) = log4(x) is vertically stretched by a factor of 8,…

A: We have to calculate resulting function after translation.

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: In class I gave a general formula for derivative of an exponential function f(x) = loga u(x) ; where…

A: use property of log function and composition function to prove the points

Q: 5. The natural logarithmic function f(x) In x has the %3D asymptote x %3D

A: Given function - f(x) = ln(x)

Q: 4. Match the logarithmic function with its graph. (a) f(x) = log2 x (c) f(x) = -log, * (b) f(x) =…

A: f(x)=log2x fx=log2-x fx=-log2x fx=-log2-x

Q: The graph of the function f(x)=log2(x) is stretched vertically by a factor of 6, shifted to the…

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Q: (a) By drawing the graphs of the functions f(x) = 1 + In(1 + x) and g(x) = in a suitable viewing…

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Q: 1. Below shows the graph of y=2* ,sketch the graph of (a) (b) y=log, x (c) y=log, x 4 3 2 -4 -3 -2…

A: If you have any doubts in the solution please ask me  in comments i will reply you as soon as…

Q: 2. Consider the logarithm function ln : (0,00) → R. Decide whether this function is injective and…

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Q: Find the equations of the tangent and normal lines to the graph of the natural logarithm function at…

A: Slope of the tangent line is the derivative of the given function at the given point. Now…

Q: 8. Without a calculator, match the functions y = 2, y = e, y = 3, y = In x, y = log x with the…

A: Without using a calculator, to match the functions, y=2x, y=e-x, y=3x, y=ln x, y=log x with the…

Q: The natural logarithmic function f1x2  ln x has theasymptote x 

A: Graph of f(x):

Q: Suppose that some points on the graph of a function f(x) are plotted on a scale in which the x-axis…

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Q: When log y is graphed as a function of log x, a straight line results. Graph the straight line…

A: Given that, the plot is between logx and logy. So, the co ordinates are in the terms of log values.…

Q: Suppose y = m In(x) + b is a logarithmic function that has the points (16.9,1.2) and (55.8,9.8) on…

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