1. Find the natural logarithm of the following when z equals: 1. -10 ii. –3 – j4 jii. 0.6 + j0.8

Q: Show that the following functions are harmonic in x and y: log√x² + y²

A: Solution

Q: Express the following logarithms in terms of ln 2 and ln 3.a. ln 0.75                 b. ln (4/9)

A: (a) ln 0.75 = ln (3/4) = ln 3 - ln 4 = ln 3 - ln 22 = ln 3 - 2 ln 2 Hence the answer.

Q: Find dx by first using algebraic properties of the natural logarithm (x+7)(x + 8)³ (x + 2)°(x + 3)°…

A:

Q: Given that ln(5) = x and ln(7) = y, express the given logarithmic value in terms of x and y.…

A: Given that ln(5) = x and ln(7) = y. Use the property of the ln function

Q: - The property of logarithms states that log for positive real numbers b, x, and y, where b + 1.

A: According to the Quotient rule property of logarithm: logamn=logam-logan,    m,n,a>0 and a≠1

Q: 4. Find the value of x in each of the following (convert to exponential form to help!). a) logX = 2…

A: Note:  Hello User, as per company policy we should answer only for first three subparts of the…

Q: 4. Use the special properties of logarithms to solve the following equations. a. M = log„1121 b.…

A:

Q: 6. A. Apply the properties of logarithms to expand the following expressions and simplify as much as…

A: Apply logab= loga + logb           loga/b=loga-logb

Q: One of the following is True: Log() = Log(z1) – Log(z2). %3D Z2 eLogz = z if z + 0.

A: In this question, there are two options which are true.And we will be using product rule of…

Q: = (5+ cx*)** y=(5+6x*) (tan(7x)° 312 hint log.differentiat use %3D

A: logab=bloga ddxtan2ax=a sec2 ax

Q: 1. Which of the following is equivalent to y= log, x ? (1) y = x' (3) x= 7" (2) x = y' (4) y = x%

A:

Q: Express the following logarithms in terms of ln 5 and ln 7. ln 0.056

A: We have to find ln(0.056) in terms of ln(5) and ln(7) Before that, write 0.056 in fraction

Q: Which of the following represents the domain of h(t)=−log(x)+3?   (2,∞) (−2,∞) (−∞,∞) (−∞,0) (0,∞)

A: Given function :

Q: Differentiate g (†) = 4 log, ( t ) – In ( t )

A: Given g(t)= 4log3(t)-ln(t) Now we have to differentiate g(t) as shown below

Q: Express the following logarithms in terms of ln 2 and ln 3

A:

Q: Solve the following logarithm problem for the positive solution for x. 1 log, x = 2

A: Given, log4x=-12

Q: Express log x Vy/z in terms of logarithms of x, y, and z.

A: Express log x4y2/z3 in terms of logarithms of x, y and z.

Q: I. Find the natural logarithm of the following when z equals: 1. –10 2. –3 – j4

A: The general form of a complex number is given by z=a+jb, where a and b are real numbers and j=-1.…

Q: y = log (4x°)

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If we let In a = A, In y = B, and In z = C, rewrite the given logarithm in terms of A, B and C: h(x)…

A: In the question it is asked to simplify h(x) in terms of A, B, C.

Q: (1) (a) Solve the following: 1 (i) 2*-6 8. (ii) log,(x+3) =1– log,(x-1)

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: log (x2) - log(v9) + log(z4) condensed into a single logarithm is expressed as log() Select one: O…

A: Expression is given by logx2 - logy + logz4 To evaluate : Single logarithmic expression.

Q: Express the following logarithms in terms of ln 2 and ln 3. ln √13.5

A: Express ln13.5 in terms of ln2 and ln3.

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

A:

Q: Express the following logarithms in terms of ln 2 and ln 3. ln 3√2

A: Solution:- the given term is A=ln(32) as we know that  ln(m×n)=lnm+lnnand ln(a)b=bln(a)

Q: I. Find the natural logarithm of the following when z equals: 1. –10 2. –3 – j4 3. 0.6 + j0.8

A: To find the natural logarithm when z equals 1) -10 2) -3 - j4 3) 0.6 + j0.8

Q: 2 log , x + 12log, y

A:

Q: e ecse with the and of logarcdtlmc dffenatiation /-

A: We have to find the differentiation of the given y

Q: 4 Given that log m3 ~ 0.945, log m4≈ 1.192, and log m7≈ 1.674, find log mm log m (Type an integer or…

A:

Q: Express the following logarithms in terms of ln 5 and ln 7. (ln 35 + ln (1/7))/(ln 25)

A: ln(m*n)=ln(m)+ln(n)lnmn=ln(m)-ln(n)ln mn=n ln m

Q: Find the equation of the curve y=g(x)=ax+b, which osculates with the graph of the logarithmic…

A:

Q: given that ln 2 = x, ln 3 = y, and ln 5 = z, express each of the given logarithmic values in terms…

A: Given:   ln 2=x , ln 3=y, ln 5=z   To find:   The logarithmic values in ln 30 in terms of x, y, z…

Q: 3 [og,x + logy] – 2[log,a + log, V5]

A:

Q: Express the following sum and/or difference of logarithms as a single logarithm. 2 loga y+logs -…

A:

Q: Express the following logarithms in terms of ln 5 and ln 7. ln 9.8

A: The given expression is ln 9.8

Q: Q1 Given that f, g and h are functions of the variable x, differentiate (c) x+ logfog h

A:

Q: Differentiate the following logarithmic functions and show that y=ln(x+5)2≠[ln(x+5)]2

A:

Q: Find d (7ª). Type In(x) for the natural logartihtm function. dx

A: Given query is to find derivative if the expression.

Q: 13. Combine the following into a single logarithm Inz- 3 In (z + 4) + In (y)) 112

A: Follow the steps.

Q: Express the following logarithms in terms of ln 2 and ln 3. ln 0.75

A: To express ln0.75 in terms of ln2 and ln3

Q: 2) Write the derivatives of these four functions: a) 7 log8(x) b) 3ex c) 5(16x) d) 9ln(x)

A:

Q: 2. Solve for x, to one decimal place. (b) 7* = 35 %3D (a) log, 56 = x

A:

Q: 4. Solve the following natural logarithm for x: In (e?) = x A. 2 В.х C. e* D. In x O A O B

A: We have to find

Q: Express the following logarithms in terms of ln 2 and ln 3. ln 3√9

A: To express:  ln 3√9 in terms of  ln 2 and ln 3.

Q: Express the following logarithms in terms of ln 5 and ln 7. ln (1 / 125)

A: Express the following logarithms in terms of ln 5 and ln 7. ln (1 / 125)

Q: A person places $123 in an investment account earning an annual rate of 2.8%, compounded…

A: Explanation and solutions is given below....

Q: If r (x) = log(x – 3) and s(x) 2 log x, which function represents (r + s)(x) ? |

A: It is given that, rx=logx-3  and  sx=2logxWe have to find the value of r+sx