b. (3e* C. z? – 2z = log(-2), Calculate the value/s of z

Q: r cos? TI Using the properties of the natural logarithmic function, expand In Vr? +1

A:

Q: Find the first six terms of the expansion of the function e^x log(1+ y)

A: We have to find the first six terms of the expansion of the function              exlog1 + y Here ,…

Q: e In 11 – log 33 ™ + log 100

A:

Q: Q3/ Evaluate the followings: 10 log,o(10z) 4) J/10 dx

A: Answer

Q: Q2: Solve the Logarithms Equation. logtan nz (2 + 4 cos ?nx) = 2

A:

Q: Calculate f dr for all p > 0 C a (log(

A: In this question, we have to check the given integrals are convergent or not. ∫01/21x(log(1x))pdx ,…

Q: y = log,(8th): In2)

A: Given,          y=log28tln2

Q: If loga = logx – 2(logy + logz), then a is equal to O Ax-y²z? В. Х v²z? O C.x-2y+2z OD. X 2y +2z

A: given,

Q: Q2/ Answer only one: al show that Log(z) = Log z+ i(arg(z)+2zk). %3D

A: The given problem is to show the given complex identity Log(z)=Log|z|+i(arg(z)+2πk).

Q: (a) Find if y(x) = log3(729) sec(In(r)) + In()r+ e

A:

Q: (b) Show that u(#) = log log (1 + l#|") belongs to W(U) but does not belong to L(U).

A: Given: u(x)= log log(1 + |x|^-1 )

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

A: logab=bloga ddxtan2ax=a sec2 ax

Q: snip

A: The exponential function and the logarithmic function is strictly increasing functions for x > 0.…

Q: b) Expand log(a+h) by Taylor's Theorem.

A: Consider the expression: loga+h ……1

Q: 3. Evaluate gloE, 54 A. 54 B. 486 С. 6 D. log, 54

A:

Q: 2 Which of the following is equivalent to log.(m) - logm(20)? F 5 G 80 log(5) log(m) K log.20

A: This can be solved by logarithm properties

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: Q7. Differentiate with respect to x: (a) log (x), *). cOS X

A: 7(a) Given- logcosxsinx To find- The derivative of the above expression with respect to x. Identity…

Q: If log, (8) z 0.7 and log, (7) z 0.6, find the approximation of log,(448) =

A: Follow the procedure given below.

Q: In the function y = log, (x +3), what is z in terms of y? O = 2 -3 O = 2 +3 O =3-2 O = 2y+3

A: Explanation of the answer is as follows

Q: 4 Given that log m2 ≈ 0.59, log m4≈ 1.18, and log m6~1.525, find log m 4 log m (Type an integer or a…

A: Explanation of the answer is as follows

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: Find the largest value of z that satisfies: loga (z) – log,(z + 3) = 8 %3D

A:

Q: Express the guven auantity In (xt2)" single logarithm. ' + I LIn x-In (x? + 3x +a)°J as a

A:

Q: what is the log trans formed. form of t

A: Given,         V=aPb

Q: - Use the fact that d In x/dx = 1/x, as well as the change-of-base theorem for logarithms, to prove…

A: Given : d lnxdx = 1x d logaxdx = 1xlna

Q: 2 log , x + 12log, y

A:

Q: (b) 8[log(2-j3)]e

A:

Q: . if võ =o, i =1 and Ju = 2 estimate 13 %3D by constructing Logrange polynamial, Itn with the exact…

A:

Q: -Given that p log, 5, q log, 2 express the following in terms of p and/or q. log, 0.625

A:

Q: (ii) Form the PDE by elimınatıng arbitfary log z=a log x+ V1-a' log y+ b

A:

Q: For f(z) = 3e6'the value of log(f(z)) is

A:

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

A:

Q: Find the exponential function f(x)=a^x that passes through the point (3,343) and has a y-intercept…

A: We have to find the exponential function f(x)=a^x that passes through the point (3,343) and has a…

Q: Given that log a 2, logy 3 and log z = 4 find log () %3D %3D O 13 8. 7 O11

A: given: we have to find the value of .

Q: d -log(z) = dz (Z

A:

Q: question b

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Q: log,(c) = m

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: 2. Given p = 2' and q = 2', express log, p'q in r and t terms. 64

A: Given

Q: find δƒ/δx and δƒ/δy. ƒ(x, y) = logy x

A: Given that: fx,y=logyx To calculate δƒ/δx Partial derivate the given function with respect to “x”…

Q: d -log(z) = dz z O O 2- 1

A: We need to differentiate the function log(z) with respect to z. Differentiation is the process of…

Q: Sind dix/dy ifLys loge vitx? 4.

A:

Q: Given that: toge C4-1)+ Log4 )=Z and Log, Cyt1)+LogE2= Show that 42-1+8² and find the Pessible…

A: We are given: log4y-1+log4x2=Z⇒log4(y-1)x2=Z⇒4Z=(y-1)x2Now,Z=1⇒(y-1)x2=4⇒(y-1)(x)=8 ---(1)Also we…

Q: Which of the following is correct? A. O log n EO(Vn) B. O vn EO(log n) C. O log n EO(Vn) D. O log n…

A: We first expand log n to see the behavior.

Q: y = log,(x + 3)

A:

Q: Find for the following function: 3- y = log,(x - x) 4- y = In2

A: It is an important part of statistics . It is widely used .

Q: Given that log z = 2, log y= 3 and log z = 4 find log () %3D %3D %3D O 29 O 25 O 31 O 26 O 27

A:

Q: t(z)= 2z log2z  , t '(z)?

A: