Differentiate with respect to x:* y = log, (x) :() 2+ In x - In x Option 2 Option 3 2 - In x 1+ In x 2() x2 Option 1 Option

Q: Assume that x,y,z and b(b)!=(1) are positive numbers. Use the properties of logarithms to write the…

A: The given logarithm expression -3logbx-2logby+12logbz. We have to rewrite the given expression.

Q: For any real number b > 1, and any real numbers x True False log, (x - y) = > 0 and y> 0, it must be…

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Q: For all values of x > 4, log (x + 4) + log (æ – 4) = log (2x) True False

A: logx+4+logx-4=log2x

Q: Find the dom ain of defination of each of the following functions: f(x)=log{1- log,,(x² - 5x +16)}.

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Q: sketch thr graph of y=4*x3 on a log-log plot. Label two points

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Q: logs(x) if 3 s x 56 if 0 < x < 3 +1 if -2 s*s0 x-2 Let f(x) = %3D x+1 Find f ().

A: Given fx=log5x2if 3≤x≤6x-2x+1if 0&lt;x&lt;3x2+1if -2≤x≤0

Q: Deduce that log (1 + x) 0. If fix) = log (1 + x), x > 0, uning Maclaurin's theorem, show that for…

A: Given that: fx=log1+x, x&gt;0 To show  log1+x=x−x22+x331+θx3 for 0&lt;θ&lt;1 and log1+x&lt;x−x22+x33…

Q: For each statement, indicate if it is True or False. Assume x and y represent positive values. v…

A: ?As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly repost…

Q: +y du show that x- + y = 3. %3D Ifu(x,y)=log x+y

A: we have to show that the following

Q: dy = (x +y – 1) + ¥+y log(x +y)

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Q: Determine if the following statements are True or False. Assume all values of the variables and…

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Q: Let b be a real number. By considering properties of exponential functions, show that the points…

A: We know, for any real number b &gt; 1,         b0 = 1      =&gt; logb(b0) = logb(1)       =&gt;…

Q: If log, æ = 0.63, log, y = 1.46, and log, z = 1.77, loga

A: As we know that, The logarithmic properties: 1). logaxb=b·logax 2). logaxy=logax+logay 2).…

Q: Prove that log(x + y) = log(x) + log(y) if, and only if, y = 1, where x > 1.

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Q: Draw and precisely write as a set, the 1-sublevel set of e^x and the 0-superlevel set of log(x),…

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Q: What is the sum of the exterior angles of any polygon?

A: See attached file for a step by step explanation.

Q: Which of the following functions are qx²)? ☐ 1x) = 17x + 11 (x) = x² +1000 f(x) = x logx (x) = x^/2…

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Q: Express as a single logarithm and if possible simplify

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Q: Prove: log,) = log, x - log, y.

A: Given: The given expression is: logaxy = logax - logay

Q: When do we use the Chain rule in derivates of exponential function

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