п/4 Show that log(1+ tan8)d = log2. 8

Q: Solve th equation for x. 22/log5x = 1/16

A: The logarithmic function is defined as the anti function of the exponential function. The…

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

A: Use property of log :→n ln(m) = ln(mn)→ln(m) + ln(n) = ln(mn)→ln(m) - ln(n) = lnmn

Q: Solve th equation for x. log2(log3 x) = 4

A: Consider the given: log2log3x=4Using log Rule:logap=n is equivalent to p=an,log2log3x=4…

Q: Use the properties of logarithms to write the expressions in as a single term. ln sec θ + ln cos θ

A: Given                 ln secθ + ln cosθ  So,    as           ln x + ln y =ln xy

Q: Express irrational solutions in exact form and as a decimal rounded to three decimal places. log2 (x…

A: Given: The equation  log2(x+1)-log4(x)=1

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

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

Q: Since the data obtained as a result of 5 observations of an experiment is ∑ log Xi = 6.27, what is…

A: n = 5 ∑ log Xi = 6.27 We have to find the geometric mean.

Q: Use properties of logarithms to expand the logarithmic expressi +2 In (x+2) X VX+2 In %3D (x+2)3

A: using property of logarithmic

Q: 2 Solve log, (2 sinx) + log,(cosx) =-1, for 2n<x<-

A: According to Bartleby's guidelines. We are allowed to solve only 1 question ata time. Apologies for…

Q: Which of the following functions grow faster than ln x as x→∞?Which grow at the same rate as ln x?…

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Q: Differentiate the following functions: 1. y = tan(log25x) + x. log3(sec x) 2. logyx = logxy %3D

A: We havey=tanlog2 5x +x.log3 (sec x)Let  u=tanlog2 5x     and    v=x.log3 (sec x)Now y=u+vdiff.…

Q: 1. Show that (a) Log(-ei) = 1 - ži;

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Q: Differentiate: 4. y = 6* log7 x

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Q: The union of left ray topo log y and right ray top log y on real numbers is usual topo log y True…

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Q: Solve for x: 9. -log3 x = – 10 = x You may enter the exact value or round to 4 significant decimal…

A: Given:       95log3x=-10

Q: 7. Use linear approximation to approximate the value of log(99) without the need for a calculator.…

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Q: Express sinh-1 x in terms of logarithms.

A: Let  y=sinh-1x⇒x=sinhy

Q: Estimate the error in the value log 2.7 obtained from the following dată.

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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: Express irrational solutions in exact form and as a decimal rounded to three decimal places. log16 x…

A: Given logarithmic equation is: log16 x + log4 x + log2 x = 7 We have to solve for x.

Q: Evaluate the integral ∫log2xdx.

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Q: Find the intervals in which ,* is increasing or decreasing logx

A: use the first derivative for finding increasing and decreasing intervals.

Q: IF LOGnB^2= 5 determine the values for logbN^3

A: Please refer the attached image for complete solution.

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

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

Q: Differentiate: 3. y = log₂ (x¹ - x)

A: y = log9(x4 -x) here logerithmic function is given  dlogax/dx = 1/x(lna) use this formula and chain…

Q: 2. Evaluate sin2x logtanx dx

A: Use the property of the definite integral and simply solve it.

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

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Q: Solve for all valid x: 2log(x) = 1+ log(x+ 1) Attach File

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Q: Find a real root of 3x – log10 x – 8 using the Successive Approximation method. Correct to four…

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Q: Verify the identity by transforming the lefthand side into the right-hand side.

A: Given expression: logcosecθ=-logsinθ The objective is to verify the left hand side equal to right…

Q: 5log(8)-1 log(x)

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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: Find a number x such that log3 (5x + 1) = 2

A: We have to find x

Q: 31. log10.x = 1 + log10 Vx

A: In this question, we need to solve the given logarithmic equation. log10 x = 1 + log10x

Q: Solve for using the definition of logarithm: (logx+29)- 2=0

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Q: Evaluate sec(log x) -dx x In | sec(log x) + tan(log x) | +C 1 log e In | sec(log x) + tan(log x) |…

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Q: Since the data obtained as a result of 10 observations of an experiment is ∑ log niXi = 8.2431, what…

A: The geometric mean of this experiment is, G=Antilog∑logniXin=Antilog8.243110=Antilog0.82431≈2.2803

Q: 2. What is the extraneous root of 2 log3(x + 4) - log3(-x) = 2?

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Q: Why is  the logarithmic function  not defined for negative values of x, thesoftware can produce only…

A: The definition of logarithmic function is, logbx=y⇒by=x The output value of exponential function by…

Q: Show that 3 logVx + 2 log x –; logx = 3 log x 2

A: Given equation is  3logx+2logx-12logx=3logx

Q: Give 5 example of integrals yielding natural log functions with solution

A: The integral examples are:

Q: what is intergral log x /x

A: WE HAVE TO INTEGRATE

Q: 1. Express logx m + log, n-Glogx m- log, n): as a single logarithm.

A: As per our guidelines we are supposed to answer only one question, kindly repost the remaining…

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

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Q: Express irrational solutions in exact form and as a decimal rounded to three decimal places. log5 x…

A: Express irrational solutions in exact form and as a decimal rounded to three decimal places. log5 x…

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

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Q: Use the properties of logarithms to write the expressions in as a single term.

A: Given: ln sin θ - ln sin θ5 To write: Using the logarithmic properties to write the given…

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…