x+4 aluate / *dx x-. None x + -1.log(x – 5) + C r+ 5 loa(r + 5) - C 5 loa(r

Q: (x cos x (а) у — etan(x³) + log;(e7 – x)

A:

Q: (x – 2)2 sin(2x2 – 3x – 2) lim log1 r+2+ 3

A:

Q: √x² ²+1{log (x²+1)-2log x} Evaluate: J- X dx

A: Given integral ∫x2+1logx2+1-2logxx4dx. The objective is to evaluate the integral.

Q: Given that 4.0 4.2 4.4 4.6 4.8 5.0 5.2 y 1-3863 1-4351 1.4816 1-5261 1.5686 1.6094 1.6487 5-2 3…

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Q: Find the greatest integer less than or equal to log29 S2²10 log₂ (x³ + 1) dx + S₁ 3 (2-1) dx.

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Q: If X~U(0,1) then Y=-In{1-X)~ Exponential (^) Pleose Show

A: When two random variables are connected by a bijective mapping and the probability density function…

Q: 4e3x+3-7=53

A: Hi! You have posted multiple questions. So, we will be solving only the first question as nothing is…

Q: 10. | [3 - e-lxl – cos x + log(x²)]dx = 0 x³ +4x – sin x 11. x² – 7 -dx 3 0

A: 10. ∫a53-e-x-cosx+lnx2dxEliminate absolutes =∫a53-e-x-cosx+lnx2dxApply the Sum Rule:…

Q: Find if z = log2 y – 6 log5 y. dy dz dz In- dy y In 10 dy y ln 10 Option 1 Option 4 64 dz In- 64 dz…

A: We know, ddxlogax = 1x·ln a a·ln b = ln ba ln a - ln b = ln ab

Q: Given that log4(y-1)+log4(x/2)=z and log2(y+1)+log2x=z-1, Show that y2=1+8z and find the possible…

A: Concept: Logarithm base change rule: logb(x) = logc(x)  logc(b) Logarithm quotient rule: logbxy=…

Q: (iv) log, r – log,(r – 1) = ; (v) 41-z = 32r+5 () -- (vi) 2x In = 0

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Q: where y = 0.5772156 Show that I' (1)-log py+log p HI = L{log x; p) Р р is Euler's constant.

A:

Q: 1-In (-) + In(2x) = In3 2- 4 log 2 - log3 + log16 = x 3-Expand In [x? sin x /Vx2 +1]

A: To find the value of x

Q: 6. h(t)=- 2-1 7. g(x)%= 1-Vx-2 8. f(x) tanx 9. (x) = log(1-2x) 10. y (1-x

A: Please check step 2 for the solution.!

Q: Solve the differential equati on. dz (log x) = –(log z) dx X

A:

Q: e3+j4(3+ j4)5 log ji' sin(3 + j4) j2022

A:

Q: d Find (3"). Type In(x) for the natural logarithmic dx function.

A: we have to find the derivative of 3x

Q: dx aluate: :S₁ (x+1) log(x+1) A In10 In[log(x+1)] + C 1 B -In[log(x+1)]+C In 10 O In 10 log² (x + 1)…

A: Topic:- application of integration

Q: (1) If the general solution of the PDE is Zr e+g(x-logz) then find the PDE.

A: By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: 2 -3 r- 3 x = %3D (z + 4)- 1 = 24 --- log, 15625 6 X = !!

A:

Q: +2=0 (p) (e) In e -lna4 In 3 In r 4 In 3 (f) log16 Vr +1 = 4 %3D

A: In these equations x value exists only if the equation is valid.

Q: dy : Prove that dx or ỹ for expression y log2(x²) is equal to ỹ = 2[1-log2 x² In 2] %3| x2 x³ In 2

A: Given, y = log2x2x2    We have to prove dydx or y¯ = 21-log2x2.ln2x3ln2

Q: 1+ax dx Evaluate log 1-ax x 1-x

A:

Q: write the logarithmic equations in exponential form.

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

Q: [E] Prove with usual notations that (i) hD = log(1 +A) = – log(1 – V) = sinh '(u8)

A: We will prove the following result.

Q: 2 lim log 10* X-1 8. -3 lim log,(x-2) x-9 А. 3/2 В. 2/3 C. 1/3 D. DNE

A:

Q: 2 2- X The integral loge dx is equal to

A: Introduction :

Q: The table shows corresponding values of x and y obtained experimentally. By drawing a suitable graph…

A: Estimate the logarithmic values of x and y. Tabulate the values of x, y, log10x and log10y.  x y…

Q: 19.) [(ycoth y² )log°(sinh y² )dy

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Q: 7) y= log, x+ 9 8) y= log, x

A:

Q: Let f be a function with f (3) = 1 such that all points (x, y) on the graph of f satisfy the…

A: This is Separable differential equation

Q: d.) In (z+9)– In z = 1 2 log Vx? + 21x = 3 e.) In(x+1) c.) In (x –1) = 2

A: (d) To Find: The value of x. Given: The equation is ln x+9-ln x=1. Formula used: ln a-ln b=ln ab If…

Q: 1-coth² (log₂x) dx x cosh(log₂x) 1. 11/20

A: We have to find the integral.

Q: 13. Integrate the following: a. b. (3-7x)6+ log 4 (2x - 5) 27 9 + 2x [ 74X_ cos(1 + 3x) + - + dx 5…

A: To evaluate give integration.

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

A:

Q: 4. Express the following single logarithm: as a i) log3 54 -log3 6 ii) 2 In (5a’b) – In (125 aº b²)…

A:

Q: 4.) Find y': Given:y = x²(3 cosh x - 1) 5.) Find y': Given: y = log, csc h (6x³)

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Q: dy Example 1: Solve x- +y= logx dx

A:

Q: 6. In (x + 8) + In (x – 1) = 2 In x 7. log3 (log, x) = 0 8. In V = Vĩn x

A: We can solve this as follows:

Q: 7. Find y'. y = log, (9– x-x)

A:

Q: rewrite each expression as a singlelogarithm.

A: 35). Given expression is 3log2x+log2y To rewrite the expression as a single logarithm. Solution:…

Q: -[In(x³/6x +5)]. dx Evaluate HINT: Use the properties of the logarithm before differentiating. 3. 3…

A:

Q: 1+logx 2. =D1. %3D 1. 196 16. Solve for x, 5-log:

A: We have to solve for x .

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

A: We have to prove the result.

Q: 4. y = log v2x + 55. y = In(2x + 1)*6. f(x) = In(x +3)* %3D

A: topic - derivative of a function

Q: 1. Find for the following functions : dx 2x (ans.: 3x' log,( 3 – 2x)-’ (3–2x )In 2 45) y=x' log,(3–…

A: