Find the domain of the logarithmic function. f(X) = In (x² = x-6)

Q: he logarithmic function f(x) = log x is transformed to g(x) = log(x + 1) + 3. Which of the…

A: solution

Q: Find dx by first using algebraic properties of the natural logarithm (x+7)(x + 8)³ (x + 2)°(x + 3)°…

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Q: e-2x 2+x In 3x csc' x -) f(x)=. b)Use logarithm to differentiate: y = (3х-1)

A: a)f(x)=ln(3x)csc2x-x5e-x3f(x)=sin2x. ln(3x)-x5e-x3differentiating w.r.t…

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

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

Q: Solve the logarithmic equation for x. log3(x + 15) - log3(x - 1) = 2

A: log3x+15-log3x-1=2

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: Find the domain of y = log(2 – lx). The domain is:

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Q: A logarithmic function w(x) = logs(2x – 1) where b is either 3 or 9.

A: Given logarithmic function is  wx=logb2x-1

Q: A/ Certain values of x and log1o x are (300, 2.4771), (304, 2.4829), (305, 2.4843) and (307,…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Determine whether f <<g or g<< f (or neither) for the functions f (x) = log10 x and g(x)…

A: Convert both lnx and log10x in terms of logx

Q: The domain of the logarithmic function f(x) = loga xis_________

A: to find the domain of the logarithmic function

Q: Use the definition of the logarithmic function to find x. (Simplify your answer completely.) (a)…

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Q: Solve the logarithmic equation for x. In( x - 1/2) + In 2= 2 In x

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Q: Find the domain of the function. g(x) = log(2 + x - x2)

A: Given, gx=log2+x-x2

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: If f(x) = 3 log4 (x+2) - 1 and F(g(x)) = g(f(x)) = x, then what is g (x)?

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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: 4. The domain of the logarithmic function f(x) = log, x is

A: fx=logax

Q: The natural logarithmic function f(x) = In x has the asymptote x =

A: Given: f(x)=lnx To Find: Asymptote of f(x). Concept: Vertical Asymptote: x=c is called vertical…

Q: f(x) − log2(1 - 3x)

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Q: Find the domain, range, x- and y-intercept of  f(x)=log3(x+3)-2 f(x)=ln(2x+2)-1

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Q: Find the domain and range of the functions f(x) = log x2 and g(x) = 3 log x

A: Given: fx=log x2 and gx=3log x   To find: Domain and Range

Q: Give five examples of exponential functions in the form f(x)=bx and f(x)= a*bP(x)+h with its domain…

A: we have to give five examples of exponential functions with its domain and range.

Q: The logarithmic function f(x) = In(x – 1) has the asymptote x =

A: Given: fx=lnx-1 we know that lnx has the vertical asymptote x=0 similarly, given function has the…

Q: Find the exponential function  f(x) = Ca^x whose graph goes through the points (0,2) and (2,8)

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Q: The function f(x) = 6X is an exponential function with base ; f(-2) = , f(0) f(2) = and f(6) =

A: base of exponential functions like ax where a is positive is 'a'

Q: Find the domain of y = log(3 - 2x). The domain is:

A: The domain is a set of x-values where the function is defined. In other words, the domain is the…

Q: use the definition of the logarithmic function to find X A) in x =3 B) in e^2 = x

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Q: Find the domain of the logarithmic function : f(x) = ln(x - 7)2

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: The graph of g(x) = log5(-x) is the graph of f(x) = log5 x reflected about the________ .

A: The graph of gx=log5-x is the graph of fx=log5x reflected about the________.

Q: The function f(x) = log16(x) is the logarithm function with base So f(16) = | , (1) = f(256) =| ,…

A: Given,

Q: First use appropriate properties of logarithms to rewrite f(x), and then find f'(x). f(x) = 2 In…

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Q: Given 2 log3(x + y) = 2 + log3x + log3 y, show that x² + y² = 7xy.

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Q: Find the domain of the function. f(x)= log %3D

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Q: 1. a) Use logarithmic properties to simplify and then find the derivative. x²Vx4 – 1 = In (x² + 1)5

A: Given function is y=lnx2x4-13x2+15. To find the derivative of the function. Solution: Properties of…

Q: Express the function f(x)=g(x)^h(x) in terms of natural logerithmic and natural exponential…

A: Given exponential form is :We need to represent t in terms of natural logerithmic and natural…

Q: Find the domain of y = log(1 – 6x). The domain is:

A: Please refer the attached image for complete solution. THANK YOU.

Q: y-loge (x+3)

A: Given: Since the transformation of logarithm is  y=logxx+3  .....1

Q: Find a so that the graph of f(x)= logaX contains the point (21,2)

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Q: Differentiate the following logarithmic functions and show that y=ln(x+5)2≠[ln(x+5)]2

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Q: Find x,where l

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Q: (b) Find the value of x: log ; x - log ; Vx = log 9- log ; 3

A: Basic concepts: remember these properties:

Q: Find the domain of the logarithmic function. f(x)=log (x-5/x+1) The domain of f(x) is ?

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Q: The domain of the logarithmic function y = log4 (x + 3) is Ox>0, XER Ox-3, x=R Oxz-3,TER OX>0, XER

A: Let's find domain of given logarithmic function.

Q: b) Find the value of x that satisfies log(x+3)− log x = log x+log 2.

A: Follow the procedure given below.

Q: 6. Find the domain of f(x) = log, [log, [log3(18r – x² – 77)]]

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Q: Use the definition of the logarithmic function to find x. In x = -1 In (1/e) = x %3D

A: First Part: Given, lnx=-1x=e-1lnex=a⇒x=eax=1e