I. Find the natural logarithm of the following when z equals: 1. –10 2. –3 - j4 3. 0.6 + j0.8 II. Evaluate the following. 1. z = ji 2. z = (1+j)¯j³ 3. z = -j3(0.6-j0.8) III. Solve the hyperbolic function of the following. 1. Find x in coshx = sinhx + 2sechx. %3D 2. Express sinh*x in terms of hyperbolic cosines and multiples of x, and hence solve 2cosh4x – 8cosh2x + 5 = 0. (x+y 3. Prove that coshx – coshy = 2sinh (2) sinh (). 4.Show that sinhz = sinhx cosy + jcoshx siny

Q: 10. fill in the missing valuesto make thė true equations . joa. Toga 7- 1o9g8= 109 a [ - 10g

A:

Q: Solve the following log functions to find the value of y:

A:

Q: 2) If x=0 and y=5 Check if the following statement is true. Explain and show your work. log, (5x –…

A: log of negative number does not exist

Q: Write the following expression as a logarithm of a single quantity. 6lnx – 10ln(x² +3) a. In(6x –…

A: Use log property

Q: 9. (log; x)² – log3 x = 3 %3D

A:

Q: Drag the tiles to the correct boxes to complete the pairs. Match each equation with its solution.…

A: We know log a + log b = log(ab) log a = log b ⇒ a=b ea=eb ⇒ a=b log a = b ⇒ a=10b

Q: Q.3. Use the Laws of Logarithms to expand the exp

A: given expression is :-logax2yz4then   by using  laws of logrithms  to expand the expression

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

Q: 60. y = (x² + 1)" (24+7)(2z+1)7 8

A: Formula used log( x )y = ylogx log( xy ) = log( x ) + log( y ) log( xy ) = logx - logy

Q: Which of the following equations is equivalent to the equation below? 6 8 a) O log, (-8) = 6 1 b) O…

A: Solution

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.