What will the coefficient (x – 1)² in the expansion of loge x about x = 1 ? %3D

Q: By using u=ln(3x) and dv=6x dx, find ∫ 6x ln(3x) dx. Be sure to include the argument of the…

A: Consider the integral

Q: How do I expand this log expression? xz/5y x times the square root z over 5y

A: We have to expand the log expression:

Q: log₂ x+1 y² √√z

A:

Q: Deduce that log (1 + x) 0. If fix) = log (1 + x), x > 0, uning Maclaurin's theorem, show that for…

A: Given that: fx=log1+x, x>0 To show  log1+x=x−x22+x331+θx3 for 0<θ<1 and log1+x<x−x22+x33…

Q: Show that for 2 degrees of freedom, the probability P of a value 1 of greater than yo is ex and…

A:

Q: Find the value of Log(-1+i) In/2 – in/3 lny2+ ίπ/4 in5-ίπ/6 ly2 +3ίπ/4

A: Solution:

Q: Use the Laws of Logarithms to combine the expressior 5 log(x) 4 ! log(x2 + 1) + 5 log(x – 1) -

A:

Q: Use the properties of logarithms to expand the given expression as much as possible

A: Use division property of logarithm

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: Find the largest value of x that satisfies: log, (z?) - log,(т+ 4) 3D 6 || | x = You may enter the…

A:

Q: 2. Evaluate, using the laws of logarithms. 2 43 log4 64 x V64* 46 256 +log,

A:

Q: (1) Expand the following into as many logarithms as possible, with what's inside each simple as…

A:

Q: 8. Use the properties of logarithms to expand the following into a sum or difference of logarithms.…

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Q: The derivate of y = 4 logx? – 5*² is | 8. 8. (2x) 5* In 5 5 x² In 10 x In 10

A: Derivative of the function

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: 2. The expression log(3 + x) is undefined for what values of x?

A:

Q: If log3 (5) = 3y, log; m² = 6 and 2 log; (4) = 4x then what expression (in terms of x and y) is log3…

A:

Q: If log (x³ (x-2)) is expanded to Mlogx+ Mog(x-2, what 3 thhe sum of Mand N?

A:

Q: Express the ratios in as ratios of natural logarithmsand simplify. log2 x/log3 x

A: Given: log2xlog3x we know that logmn=lognlogm

Q: The least value of the expression 2log10x – logx(0.01), for x > 1, is- (A) 10 C) –0.01 (В) 2 (D)…

A:

Q: If log m base 2 is x and log n base 2 is y, what is the product mn equal to?

A:

Q: 4. Solve the following logarithmic equation: log3 (Z + 8)x7 – log3 (2K + 9)x3 = log3(Z + 5)x2 + 4(Z…

A:

Q: Find the formula for an exponential function of the form f(x) = A · Bº that passes through the…

A: We get exponential function by putting  both the point one by one and then by solving thes two…

Q: If loga = x and logb-y, then log Vab is equivalent to %3D %3D

A: To find equivalent relation, we will apply basic logarithmic formulas to the given expression.

Q: In LRT reject H, when Ais small, so we reject H, when the value -2 log A is small Select one: True…

A: Answer : False

Q: الوقت المتبة The expansion of the logarithmic expression x2 In (x+1)/(2x-3) is a) Inx + In(x + 1) –…

A:

Q: Expand the logarithmic expression In(XY^2Z^3)

A: To expand the logarithmic expressionlnxy2z3

Q: Solve the following equations. log, (2.x – 3) = 3 4 In(3.x) = 8 log x = log(1-x)

A:

Q: Evaluate log2(x²) dx In(2) -log2(x²) + C 4 In(2) log2(x²) + C n(2) (log.(r2))2 (log. (x2))2 1r 4…

A:

Q: What would be the value of x in log 2 (5x-2) = 3? %D O x = 1

A:

Q: a and In 3 = b. Use properties of logarith 31. In 1.5 %3D In

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: Given that log z =2, log y = 3 and log z = 4 find log () %3D O 13 O 9 8. O 7 O 11

A: We are asked to find the log

Q: a- Simply the following 1. Inx – In(x2 – 1) + 2ln(x + 3) 2. 5log2 + log3 - log8

A:

Q: Find the integral: log2 X dx In(2)/ 082(x) + C 2

A: Put logx = u then solve it.

Q: What is the value of (log 5 to the base 2) + (log 5 to the base 3)?

A: the value of (log 5 to the base 2) + (log 5 to the base 3) is

Q: 7) use the properties of logarithms to: a, expand the expression log(x3z y2)

A: Consider the given expression log(x3z y2)

Q: Which of the following is equivalent to log( V2x+y ? (2x+y) O In (In(2x+y)-3 In y) In 10 In(2x+y) 3…

A:

Q: The exponential form of log(x)+log(y)=-2 is: x-y=10^-2 10^xy=-2 x+y=10^-2 xy=10^-2

A: This question is related to exponential and logarithmic equations, we will solve it using given…

Q: . Use the Laws of Logarithms to expand the expression.

A: We have to use the laws of logarithms to expand the expressions: a logxy3z2      b lnxy     c…

Q: 4) Use the Laws of Logarithms to expand the expression as much as possible. Vx +5 In (2x²/y/

A:

Q: Compute 3 In(e) +2 log(10) 7 11 1 9. 3. B8

A: Solve by properties of logarithm.

Q: thats a natural log of 9 to 0 and integral from 9 to e^x

A:

Q: If log2(3r + 5) = 5, then z =

A: We have to find the value of x log2(3x + 5) = 5 . So , By logarithmic properties. loga(b) = C Means…

Q: State the restriction(s) on the variable x in log(2x-5) – log (4 - x)

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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: Find a formula for the exponential function passing through the points (−2,48) and (2,3). f(x)=

A:

Q: Use the Laws of Logarithms to expand the expression. xy (а) log x + 2 (c) log V + 4) (b) In

A: We know that, the property of logarithm is given as logmn=nlogm                 ⋯⋯1logmn=logm+logn…

Q: What is the value of x in log. 3 =- ? А. 1 В. 3 С. 9 D. 27

A:

Q: If c=log 2, what is log 0.8 in terms of c?

A: