Use the definition of the logarithmic function to find x. (Simplify your answer completely.) (a) In(x) = 9 X = (b) In(e*) = x X =

Q: Find the domain of the logarithmic function :  f(x) = ln(x2 - x - 2)

A: Inside log we can not have negative number. So, x2 - x - 2>0

Q: Is ln xy = ln x ln y a valid property of logarithms, where x > 0 and y > 0? Explain

A: ln(xy)=ln(x)+ln(y) using the addition property of logarithm. Where x>0 and y>0.

Q: Find the value of x in the logarithmic equation

A: Given, 1) log24x +log29=log2722) log381=x3)log2(2x+1)<3

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

A:

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: . How is the graph of log x related to the graph of ln x?

A: Here , ln x represents the natural logarithm where its base is e whereas the base of log x is 10 .…

Q: Differentiate the function using logarithmic rules. g(x) = ln[x3√(x3+1)]

A:

Q: How is the logarithmic function y = log a x defined?

A: To define the given logarithmic function.

Q: Solve the logarithmic equation. Be su log x+ log s(7x- 1) = 1

A:

Q: In the given question , use the properties of logarithms to expand the logarithmic expression.   ln…

A: Given expression is  ln (x y z)

Q: Find the domain of the logarithmic function f(x) = ln(x - 1)2.

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

Q: domain of the logarithmic function f(x)= logax is

A: The domain of the logarithmic function f(x)= logax is given by

Q: Using properties of logarithms, we can rewrite the equation as In(y) - In(x7 cos(x)), which is…

A: Consider the equation  ln(y)=ln(x7cos(x))

Q: Find the domain of the function. f(x) = log -6

A:

Q: Use the properties of natural logarithms to simplify the function. f(x) = In(e-6x) + 9x + In(1) f(x)…

A:

Q: Find the domain of the logarithmic function.

A: We need to find the domain of the given logarithmic function.

Q: Use the properties of logarithms to expand the logarithmic expression.          ln xy/z

A:

Q: Using logarithmic differentation, find the first deruvative of h(x)=(x^6 tanx)/(e^x sinx)

A:

Q: Solve the logarithmic equation for x. log5(x + 1) - log5(x - 1) = 2

A:

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: Let log x 4, log y = 5, log z = 3. Using properties of logarithm, find the value of log Show your…

A:

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: The domain of the logarithmic functionf(x)=logax is _______.

A: We have to find the domain of the logarithmic function: fx=logax

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

A: Domain of any function is defined as the value of x for which the function is defined - Given…

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

A:

Q: Find the domain of the function. f(x) = 3 - 2 log4 (x/2 - 5)

A: Given function is: f(x) = 3 - 2 log4 (x/2 - 5) We have to find the domain of this function.

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: Differentiate f (x) = loge (x26")

A:

Q: How is the logarithmic function (x) = log2(x) related to the exponential function g(x) = 2×? The…

A: Given, fx = log2x gx = 2x

Q: Find the domain of the logarithmic function f(x) = ln(x2 - 4x - 12).

A: Given :         f(x)= ln(x2-4x-12).

Q: How is the logarithmic function y = log,(x) defined? %3D It is defined as the inverse of the…

A: the give function is  to solve for x, write b to the power both sides

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

A:

Q: Use the properties of logarithms to expand the quantity.  ln  x 2   / ( y 3  z 4 )

A: It is given that, lnx2y3z4 Use the properties of logarithms,we have to  expand the quantity.

Q: Use the properties of logarithms to expand the logarithmic expression.      ln(xyz)

A: Given: ln xyz To expand: The given logarithmic function.

Q: Why is  the logarithmic function  not defined for negative values of x, thesoftware can produce only…

A: The definition of logarithmic function is, logbx=y⇒by=x The output value of exponential function by…

Q: Find the domain of the logarithmic function : f(x) = ln(x2 - 4x - 12)

A: Our Aim is to find the domain of the logarithmic function:-f(x)=ln(x2-4x-12) -(i)

Q: Use the power rule to expand the logarithmic expression: ln √x

A: Given: lnx

Q: Use the power rule to expand the logarithmic expression: ln 3√x

A:

Q: Use the properties of natural logarithms to simplify the function. f(x) = ln(e7x) − 3x − ln(1)

A: Given:

Q: Express the function f(x) = g(x)"(×) in terms of the natural logarithmic and natural exponential…

A: Apply natural logarithm to the expressions on both sides of the given function fx=gxhx.…

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

A:

Q: Find the domain of the logarithmic function f(x) = log(2 - x).

A: Consider the given logarithmic function fx=log2-x

Q: Solve the logarithmic equation for x. log2x + log2(x - 3) = 2

A: Given equation: log2x+log2x-3=2

Q: The graph of the natural logarithmic function has a at Its domain is Its range is

A:

Q: find the domain of the logarithmic function f(x)=log2(x-1)

A: Given logarithmic function is,

Q: Use logarithmic differentiaion to evaluate f`(x) f(x) = (5x)^(ln 5x)

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.