Explanation Given information: The equation, 2 ln x − 1 2 ln 9 = ln 3 ( x − 2 ) Concept used: The equivalent exponential form of a logarithm for a > 0 , x > 0 , a ≠ 1 is given by log b x = y if and only if x = b y Exponent property of Equality : If the same bases raised to different exponents are equal to each other, then their exponents will be equal as well. That is, if a m = a n then m = n Exponent property, 1 a n = a − n Quotient property of logarithm: log b m − log b n = log b ( m n ) Power property of logarithm: n log b a = log b a n Calculation: To solve the given logarithmic equation, first write the left side of equation by using the power property and quotient property of logarithm as shown 2 ln x − 1 2 ln 9 = ln 3 ( x − 2 ) ln x 2 − ln 9 1 2 = ln 3 ( x − 2 ) ln x 2 − ln 3 = ln 3 ( x − 2 ) ln ( x

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 2, Problem 21SP

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Solve the given equation 2lnx−12ln9=ln3(x−2) for x.

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Chapter 2, Problem 20SP

Chapter 2, Problem 22SP

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

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K Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist. x-7 p(x) = X-7 Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. (Use a comma to separate answers as needed.) OA. f is discontinuous at the single value x = OB. f is discontinuous at the single value x= OC. f is discontinuous at the two values x = OD. f is discontinuous at the two values x = The limit is The limit does not exist and is not co or - ∞. The limit for the smaller value is The limit for the larger value is The limit for the smaller value is The limit for the larger value does not exist and is not c∞ or -

Chapter 2 Solutions

Calculus

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Solve the given equation 2 ln x − 1 2 ln 9 = ln 3 ( x − 2 ) for x.

Solution Summary: The author explains the equivalent exponential form of a logarithmic equation for x.

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Solve the given equation 2lnx−12ln9=ln3(x−2) for x.

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Chapter 2 Solutions