For the part circled in orange, I'm confused to why this is 4, and not just 3 in this spot because I thought the derivative took the number in front of natural log and put it in the numerator. For the part circled in blue, how do we get to L=e^12 from lnL=12. Is this an identity? Thank you.

Q: Given that log¸× = 2 3 log, Y = 5 3 determine the value of log 109 21 27 2 (주)

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Q: Y = log, (x-s) 3.

A: As we know from the logarithmic property; If logba=c;  b>0,b≠1,a≠0 then bc=a

Q: 3. Consider the function y = log.(x). A. What function is the inverse of y = log(x)? B. Give exact…

A: As per bartleby Q&A guidelines we solve only first question with its three subpart and rest…

Q: Find the roots of the equation: log(2x + 6) = 3

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Q: Solve the following equations for xx using the natural logarithm:  11⋅4^x=2e^−3x

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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 > 1,         b0 = 1      => logb(b0) = logb(1)       =>…

Q: 3. Express as a single logarithm: 3 log 2 + log x - log (4x) log(8x) A. log(4x) В. log (2) C. log…

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Q: lve log, x =2 and write out the check.

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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: Write all the steps on a piece of paper and upload your answer: Use logarithmic differentiation to…

A: Given,

Q: Determine the inverse of each function. Express in logarithmic form: A) y=3^x B) y=b^x C) y=(3/5)^x

A: Note: Let f(x) be a function and f(x)=y, then putting y into the inverse of f produces the output x.…

Q: If log, 2 = x and log, 3 = y, evaluate the following in terms of x and y: 4x+2y a) log, 144= (b)…

A: Here, given that logb2=x, logb3=y

Q: Note that your response should be written in sentences, and logically justified to gain full marks.…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: