5. Differentiate the following natural log and e functions. y = In (12 - x - 5x²1) a. b. C. y' 11 y' = || y" = y = In(e-x + xe-x) y = x² In(8x)

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A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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Q: 3 Differentiate if x* log,(2+vx) f(x)=|

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A: Defination of exponential and logarithmic function -: For a positive real number x , y=logax if and…

Q: 8.) Evaluate the following natural logarithm problems: d.) e^0= e.) e^1= f.) e^–0.475 =

A: (d) We need to evaluate e0. Using the property x0=1 for any value of x. We get e0=1. (e) We need to…

Q: . Solve the following equations. (Se 10. 3 =15 11.log (x+2) = log (3x - 5) 12.log3 (2x+ 5) = 2 13.…

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Q: 7. Solve for x using log properties: log(5x) – log(x² - 2) = 1 |

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Q: 7. Determine the general value of the following: a. In (3+j5)i b. log(-5) (6+ j4)(l+/2) С.

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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: 1. Use the definition of the logarithmic function to find x in the following equations: a) log, 25 =…

A: NOTE:- As Posted multiple independent questions,we are answering only first question as per bartleby…

Q: Show that b) logi = (2n + 2) ri лi (n = 0, ±1, ±2, ...);

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Q: Q3. Find y, b, or z as indicated (1) Find y: y = logg 27 (2) Find : log, z = -1 (3) Find b: log,…

A: To find y, b, or x as indicated.1 To find y: y=log9272 To find x: log3x=-13 To find b: logb1000=3

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Q: Which expression is equal to log a + log y – log 2? log yz O log (æyz) xy log () Olog 1. xyz

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Equation of Waves

Wave is an oscillation or disturbance traveling in a medium. It performs the transportation of energy but does not carry any matter. This motion of waves will transport fuel in a medium without permanent transfer of mass (particle).