Express In(1+r²) +In r- In sin r as a singel logarithm.

Q: (a) log,(5x – 1) + 6 = 9 (b) 163x+1 = (4)*-1 %3D (c) In(x + 6) = In(11) – In(x – 4)

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Q: Solve for x using sci notation x=log(y^5) ; if (log y) = 1.2 x 10^-4

A: We have to find value of x by using scientific notation.

Q: 3. Find syz for ys = In(x + yz) – xcoth-1 log ().

A: Given : Let us consider the given value as,  ys=ln(x+yz)-xcoth-1logzy

Q: Suppose that log, x = 5 and log, y = 4 compute %3| log, Vx²y³

A: Given

Q: Use the trapezoidal rule with five function values, together with appropriate log laws, to show that…

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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: .Expand log (1 + sin x) in powers of z as far as the term in r.

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Q: Show that S log(sin x) dx = -log 2.

A: To show that ∫01logsinπxdx=-log2 using the given figure.

Q: Find the integral: log7 X dx = %3D

A: Solve the following integral

Q: Express in terms of logarithms of x, y, z, or w.

A: Express in terms of logarithms of x, y, z, or w.  Given expression is log3 y5

Q: s) Use the properties of logarithms to find dx y = In 4] sin' (3x) 5* √√x² +1

A: We can solve the derivative of 'y' as below.

Q: Express in terms of logarithms of x, y, z, or w.

A: Given logarithmic expression is log4xz. To express logarithms in terms of x, y, z or w. Solution: We…

Q: determine the nature of functon for even and odd Ax) = log(x+ Vx² +1) ?+1)

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Q: If x2 + y2 = 25xy . Then prove that 2 log(x+y) = 3log3 +logx + logy

A: It is given that x2+y2=25xy add 2xy to both sides  x2+y2+2xy=25xy+2xy using the formula…

Q: Differentiate with respect to x:* y = log, (x) :() 2+ In x - In x Option 2 Option 3 2 - In x 1+ In x…

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

Q: (a) In (x (b) log; 2y2

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Q: Differentiate implicitly to find y' log3 (x). tan cy+ 1) = y2 %3D

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Q: Which of the following functions grow faster than In x as xoo? Which grow at the same rate as In x?…

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Q: 1 (log, x)' 3x ise b =?

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

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Q: b- find x for following 1. logx = V2 2.ln(x + 1) = 5

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Q: Express in terms of logarithms of x, y, z, or w.

A: The given expression is log3xzy

Q: B. Express as a single logarithm and, if possible, simplify. 1. log, x + 4 loga y – 3 loga x 6.…

A: This is a problem related to logarithm properties. Based on the general formula we can answer the…

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: Show that J log(1 + tan0)d= log2

A: Given that: To prove:        ∫0π4log(1+tanθ)dθ=π4.log2

Q: Express in terms of logarithms of x, y, z, or w.

A: lnx y4z53 =lnx +ln y4z53 =lnx +ln y4z513  ln y4z513 =13ln y4z5 =13ln y4-ln z5 =134 ln y-5 ln z =4 ln…

Q: Evaluate loge 7 by Simpson's (i) rd, and (ii) th rules.

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Q: Differentiate the following and simplify: y= log, (sinhe") h(x)=3sinh(1–3x² )cosh(1– 3x² ) 1. 2.…

A: As per bartleby guidelines we only give first question answers.

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

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

Q: find dy if by using logarithmic

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

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Q: Find all positive values of 'a' for which the equation log (ax) = 2 log (x + 1) has the unique root.

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Q: Find all vawes of k don uhich log kx 112 log (x+) has one soluhion

A: Just use basics of logarithm.

Q: b- find x for following 1. logx = v2

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Q: п/4 Show that log(1+ tan8)d = log2. 8

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Q: y = Arccos (logx); y' = * %3D

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Q: 2 In x + 3 In y – In z

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Q: B. Express as a single logarithm and, if possible, simplify. 1. log, x + 4 loga y - 3 log, x 6.…

A: According to our company's guidelines I can only answer first three subparts of the question B since…

Q: 2. Evaluate [log(-1-/)(-2- j2)] tan(4 + 3i) cosh-1

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Q: 3. Find syz for ys = In(x + yz) – xcoth- log ()-

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Q: ` log x dx

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Q: d log, x = 1 dx [(In a)(x)]

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Q: 4. Show that sinh-1 x = log(x + vx² + 1).

A: We have to prove the result.

Q: Evaluate So ·∙log 1+ax 1-ax (: ( dx x√√1-x²

A: A very good problem. This problem illustrates the power of differentiating under the integral sign.…

Q: Use these formulas to express the numbers in terms of natural logarithms. 61. sinh-' (-5/12) 63.…

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

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: