Using properties of logarithms, we can rewrite the equation as In(y) - In(x7 cos(x)), which is equivalent to Jance). In(y)

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: 1. Use the properties of logarithms to simplify the expressions: a) In sin 0 sin 0 In 5 b) In (4r*)…

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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: If log2 X = 5, what is ln X?

A: topic - logarithmic function

Q: Suppose that ln 2 = a and ln 3 = b. Use properties of logarithms to write the logarithm in terms of…

A: We have to write in terms of a and b by using properties of logarithm for the given logarithm…

Q: express equation in logarithmic form  e^x=5 is the equivalent to the logarithmic equastion:…

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Q: e-* = 2 log »

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

A: log3x+15-log3x-1=2

Q: log(x³) dx

A: Consider the integral: ∫logx3xdx…

Q: Suppose that ln 2 = a and ln 3 = b. Use properties of logarithms to write the logarithm in terms of…

A: Given,ln2=a,ln3=b ln(1.5) On simplifying further we get: ln(1.5)=ln(32)=ln3-ln2…

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

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Q: Use the properties of the natural logarithms to simplify the following expressions sin 0 a) In sin e…

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Q: 'x + 2 3. -dx x + 1

A: To integrate: ∫x+2x+1dx Solution: Evaluating the integral.…

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

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Q: What is a logarithmic function? What properties does it satisfy? What is the natural logarithm…

A: Logarithm Function:A Logarithm is simply an exponent that can be written in different way.For…

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

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Q: State whether the following statement is true or false. Because the domain of ​f(x)=logax is the…

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Q: Suppose that ln 2 = a and ln 3 = b. Use properties of logarithms to write the logarithm in terms of…

A: We have been given that ln 2 = a and ln 3 = b.

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: True or False If y= logax , then y=ax.

A: The given statement is y=logax , then y=ax.we have to find it is true or false.

Q: cos e Differentiate y =- using Logarithmic differentitation. nxV2x +1

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Q: Suppose that ln 2 = a and ln 3 = b. Use properties of logarithms to write the logarithm in terms of…

A: Given ln 2 = a and ln 3 = b.To find ln 27 in terms of a and bFormula:log ab=b log a

Q: 1+x2 Through the proof of the logarithmic form of the function y-cschx-In(- |x| which of the…

A: The logarithmic function is the inverse function of the exponential function. The logarithmic…

Q: Find d/dx(2^x) Type ln(x) for the natural logarithmic function.

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Q: slove for x by converting the logarithmic equation to exponential form log7(x)=-3 x=

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Q: Express the following logarithms in terms of ln 2 and ln 3. ln 3√2

A: Solution:- the given term is A=ln(32) as we know that  ln(m×n)=lnm+lnnand ln(a)b=bln(a)

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: Express cosech-x in terms of logarithm. Hence, solve the following equation and give a reason for…

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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: If p(x)=(x3+2x)^sinx, find p′(x).  Enter an exact answer in terms of a natural logarithm.

A: As the given function :- P(X) = ( X3 + 2X )sinx  P'(X) = ?

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: According to the properties of logarithms In sec x= - In cos x O True O False

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: After examining the graphs of several logarithmic functions, you should see that there are…

A: Solution

Q: If p(x)=(2x+4)^tanx, find p′(x).  Enter an exact answer in terms of a natural logarithm.

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Q: How would you find y' if x^y=y^x using logarithmic differentiation and keeping the answer in terms…

A: Given equation:The given equation is xy = yx.

Q: y = (2ª – e2") In(x²+1) ||

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Q: Solve the logarithmic equation for x. log x + log(x - 1) = log(4x)

A: Consider the provided equation, logx+logx-1=log4x Solve the logarithmic equation for x. Apply the…

Q: Solve the logarithmic equation for log x + log(x–1) = log(4x)

A: Given, log(x)+log(x-1)=log(4x) By applying the log rule, loga+logb=logab ⇒log x(x-1)=log…

Q: Use properties of logarithms with the given approximations to evaluate the given expressions. Use In…

A: The given logarithm values are ln 2=0.69 and ln 3=1.1. (a) Evaluate ln(16) as follows. Therefore,…

Q: Express the following logarithms in terms of ln 2 and ln 3. ln 0.75

A: To express ln0.75 in terms of ln2 and ln3

Q: Solve the logarithmic equation for t. ln(at + b) = c if a ≠ 0

A: To solve the given logarithmic equation.

Q: Vx²-1•sin x y%3= %3D (2x+3)4

A: To find: The derivative of y=x2-1·sinx2x+34 using logarithmic function. Formula used: The derivative…

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: When is ln x negative?

A: When is ln x negative?

Q: A person places $123 in an investment account earning an annual rate of 2.8%, compounded…

A: Explanation and solutions is given below....

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

Q: How does ƒ(x) = log x (2) compare with g(x) = log 2(x)? Here is one way to find out. a. Use the…

A: We have the logarithmic identity,