Does the function f(x)= logarithm x with the base of 1/2 approach a certain real number as the value of x increasing positively? What is that real number?   ... Does the function f(x)= logarithm x with the base of 1/2 approach a certain real number as the value of x ap

Q: Find the exponential function f(x) = ab^x that satisfies the conditions f(0) = 1 and f(3) = 27.…

A: Given conditions, f(0)=1    and    f(3)=27 f(x)=abx                   ....(1)

Q: The half life of substance A is 18 years, and substance B decays at a rate of 30 % each decade. (a)…

A:

Q: If the base  b of the exponential function is a real number between zero and 1  (0 < b < 1 ) , then…

A: Exponential functions have the form f(x) = bx, where b &gt; 0 and b ≠ 1. Just as in any exponential…

Q: The Gutenberg–Richter Law states that the number N of earthquakes per year worldwide of Richter…

A:

Q: For the function f(x) = 2 log(x): %3D f'(2) = %3D f'(5) = For the function g(x) = 3x + log(x): %3D =…

A:

Q: Find the exponential function of the form h(x)=ba^x + c such that  y=2 is a horizontal asymptote…

A: Topic:- calculus

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) =…

A:

Q: Is f(x) 0 in the range of the functionf (x) = log(x)? If so, for what value of x? Verify the result.…

A: Given function, fx=logx To check fx=0 in the range of the given function, for what value of x.

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

A:

Q: A utility company in a western city of the United States expects the consumption of electricity to…

A: Given: A  utility company in a western city of the United States expects the consumptionof…

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: Consider the function f (x) = log10 x.   Find the ratio of x1 to x2  given that f (x1 ) = 3n and f2…

A: Solution:x1 Consider the given log function. f(x) = log10x For x1,  f(x1)  = log10x1 we have given…

Q: The graph of the function f(x)=log10(x) is stretched vertically by a factor of 3, reflected over the…

A: Given: The parent function is f(x)=log10(x). Transformations: 1) Stretched vertically by a factor of…

Q: A function defined by y = ab can be written in terms of an exponential function base e as

A: The function is y=abx

Q: Prove that the straight line y=3-2x intersects the exponential curve y=e^x at a point whose…

A: Please refer to the image below

Q: 4. Determine the co-ordinates of the point of intersection of the graphs of f(x) = 5(3*) %3D log a…

A: The given curves are  f(x) = 5.3x f(x) = 7.2x

Q: How are the functions ax and log ax defined? Are there any restrictions on a? How is the graph of…

A: Proving that both the functions are defined. Logarithmic functions are the inverse of exponential…

Q: 4. f (x) = log2 x and g(x) = vx – 4. What is the domain of f( g(x))and g(f(x))?

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Q: a) Express the new function h(x) = log2(x + 2) in terms of the original function f (X) = log2(x).…

A:

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

A: Prove that limn→∞ ln xxP=0for any numbers P&gt;0

Q: For the function f(x)=5.log (x* - 10x +x+30)-5, on the interval (-4, 4), approximate the local…

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Q: 14. Find the domain of definition of the function 31 Vx + 5 X-5 y = log10 (,2 x² – 10x +24

A: The domain of a function is the set of input or argument values for which the function is real and…

Q: The graph of the function f(x) = log6(x) is stretched vertically by a factor of 3, reflected over…

A:

Q: Prove that the straight line y = 3 - 2x intersects the exponential curve y =e^x x at a point whose…

A: y=3-2x  and  y=exat f(x)=3-2x-ex

Q: Does the function f(x) = 2e¯X represent exponential growth, decay, or neither? A) Exponential growth…

A: Here we will apply the concept of increasing and decreasing function to come to the conclusion

Q: Differentiate. a) f(x)=ln(e^x-x^3) b) g(x)= ln x/e^x c) f(x)= log20^x

A: a) Differentiate the given function as follows. f'x=ddxln ex-x3=1ex-x3ddxex-x3…

Q: Find a formula for the exponential function passing through the points (– 2, 40) and (1, 5) f(z) =

A: Consider the exponential function y=abx. Substitute -2,40  and  1,5 in the above function and obtain…

Q: (a) Use the definitions of hyperbolic functions in terms of exponentials to prove that 8 cosh'x cosh…

A: a) LHS =  8cosh4x  =  8(cosh2x)2  =  8 * ((1/2)( cosh(2x) + 1))2  =  2 (cosh2(2x) + 2cosh(2x) + 1)…

Q: 1. When the interest on an investment is compounded continuously, the investment grows at a rate…

A: The change in amount with the rate r is dPdt=rP The amount of investment is 20,000. The amount of…

Q: Given the functions f(x) = log₂ (2x) and g(x) = 2x - 3, which of the following statements is true?…

A: Here, the given functions are f(x)=log2(2x) =ln (2x)ln 2(used change of base)&amp; g(x)=2x-3 Here,…

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: Determine whether the following statements are true and give an explanation or counterexample.

A: Given information:

Q: Find the exponential function f(x) = ab² that satisfies the conditions f(0) = 2 and f(2) = 8. f(x) :

A: Topic:- algebra

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

A:

Q: Find the exponential function f(x) = ab® that satisfies the conditions f(0) = 2 and f(-3) 4 f(x)

A:

Q: 2. Compute for the value of x in a given logarithmic inequalities loga(x+1) > log:(x2). a. x > ½ b.…

A:

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: FInd the Domain of these functions. f(x) = log7 (4x + 8) f(x) = ln(4x − 20)

A:

Q: =) Express the new function h(x) log2 in terms of the original function f (x) log, (x).

A:

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: Find the range of the function x* +e x+e f(x)%3sin{log, +cos {log. x' +1 2 x*+1

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Q: The half life of substance A is 22 years, and substance B decays at a rate of 30 % each decade. (a)…

A:

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

A: Given function - f(x) = ln(x)

Q: a) Express the new function j(x)=log(−x)−4 in terms of the original function g(x)=log(x)−4.  g(x)=

A: Given functions ,   j(x) = log(-x) - 4                                 g(x) = log(x) - 4

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

A:

Q: True or False The graph of f(x) = loga x, where a &gt; 0and a ≠ 1, has an x-intercept equal to 1 and…

A: Given function is, fx=logax, where a&gt;0 and a≠1.   Use the properties of logarithmic function, The…

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

A: Graph of f(x):

Q: 3) For f(x) = log2 x and (x)=√x-4, what is the domain of f(g(x)) and g(f(x))?

A: The function f(x)=logx is defined for x&gt;0 The function f(x)=x is defined for x≥0 Note: If logba=c…

Q: that the logar log x, and f(x) = In x have in common and the attributes that make them different.…

A: The difference between log and ln is that log is defined for base 10 and ln is denoted for base e.