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 dy y ln 2 ln 5 dy y ln 2 In 5 O Option 2 O Option 3 ||

Q: 4 If y = x, then F z = log.y G y = log,z H x = logry z = log,x

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Q: More models For each of the models listed below,predict y when x = 2.a) yn = 1.2 + 0.8 log x d) yn2…

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…

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: Find y’ when y^2 e^2x = 3y + x^2 and y(0) = 3 a. -5 b. -7 c. -6 d. -4 e. -2 f. -1 2. Find the…

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Q: Find Y and simplify whenever possible. dx 1. y = log v2x – 8 6. y = log V12x 2. y = In -1 7. y = x**…

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Q: In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as…

A: Hello. Since your question has multiple parts, we will solve the first three questions for you. If…

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

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Q: 1) Find dy/dt for if : y = log2 (87ln 2)

A: Apply differential rule to solve 1st question [ln(u(x))]'=1u(x)u'(x) power rule [x(n)]'=nxn-1 Apply…

Q: A triangle has variable sides x,y.z subject to the constraint such that the perimeter is fixed to 24…

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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: dw Find if w = x10 + 10*. dx log 10 dw dw 10 10x° + 10* 10x° dx dx log10e O Option 3 O Option 1 dw…

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

Q: dz dz +y дх = 50 +x4°y+y5° ), Prove that x ду If z= log (x50

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Q: Find dy/dx. Do not simplify the answer. 4* +4 csc a.) y = log4 x-csc(4) b.) x3 y + cosh¬1 3 = e –…

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Q: а. (у + 2)2— 2x log y - In u = 2e-x, k > 0 ay ax? ду? b. uxx + xy uxy + y²u² = 0 = v2 + x azu C. t-…

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Q: 19. If logx y + log, x = 2.9 and xy = 128, find x + y. 24 O 20V2 O 36 O 34V 2 O 66

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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: Suppose that a certain population obeys the logistic equation dy = Ty dt K a) If yo K find the time…

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Q: log x y = dy dx 5+5ln5logx x² In5 dy 5-5ln5log x dx x² In5 Option 4 Op tion 3 dy _ 5-5ln5logx x² In5…

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Q: Find ay dx 3. 4. 5. y = 2e³x5tanhx y = xln(5x-2) y = sec ¹(log 7x)

A: Given :y=2e3x5tanhx4. y=xln(5x-2)5.  y=sec-1log7x

Q: 3. If 19.4 = log (ab) and 7 = log₂ (a), where > 1, then log, (b) equals H 12.4 26 2.8 135.8 ◄ Prev…

A: We want to find the value of logxb.

Q: If t > 0 and 3" kT, where k E Z, then 3" (2 log3 t – 1)7 (2а — 1)" -In 3. csc² (3ª ) d -- dt dæ t…

A: To determine whether the given statement is True or False.If t>0 and 3x≠kπ, where k∈Z,…

Q: Find dy/dx if y=log(-4x^2+2)

A: To find the dy/dx of the given function.

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: dy Solve the initial-value problem for y as a function of r. (4 x) = 1, y(0) = 4 de…

A: Given initial value problem is,

Q: 2. Suppose that a certain population obeys the logistic equation * - (1 -) dy = ry dt k k find the…

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Q: Match the Following: If Int – In 7 = 1 then t = Choose. If log z + log 5 = 1 then z: Choose. 23.15…

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Q: 7 log.y- log, w+4log.z 5

A: on applying log algorithm we will get

Q: Combine into a single logarithm. In(x – y) – 2 In(x² + y²) OIn (x-y)3 In (x²+y²)* In Va-y) (x²–y²)?…

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Q: dy 18. x = y (log y-log x+1) (AMIETE, Summer 2004) dx Ans. log2= Cx 19. xy logdx+| y -x² log dy = 0…

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

Q: - y =log x² dy_ 8log, x A. dx dy 4log, x В. dx dy _ 4xlog, x xIn 2 dy 8x log, x D. dx xln2 xIn2 dx…

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Q: y = log, x %3D 1 1 1 2 4 8. 16 8 4 2 y.

A: given y=log2x complete the table x 116 18 14 12 1 2 4 8 y

Q: If T = 1o, then log T is equivalent to: 5 A (1 +2 log x) – log y B log(1 +2x) – log y (1- 2 log x) +…

A: We can find the log as below

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: 2) y= log, (-4x +6)+ 4 2 +6 1) у3D 4) y= In (4x – 10) – 6 e+10 3) y =

A: SOLUTION- Since you have posted a question with multiple subpart , we will solve first three for you…

Q: Models For each of the models listed below, predict ywhen x = 2.a) ln yn = 1.2 + 0.8x d) yn = 1.2 +…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Show that || (A(st) + A(s)A(t)) dsdt = 2.x log x + 0(x) as x → 0o. JU(4)| log°x s 2 // |u() dsdı +…

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Q: At time t = 0, there is one individual alive in a certain population. A pure birth process then…

A: A pure birth process gives the successive birth times as 25.8, 42, 52, 55.8, 59.2, 63.3. The process…

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

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Q: Differentiate y = (9x- 11) log3 (1læ – 9). %3D A. y' = 9(11x-9)+11(9z-11) In(9r-11) (9x-11) In(3)…

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Q: If y = log x + ex then dy/dx = log x + ex a. True b. False

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Q: Differentiate y = 3e +7 ln(2x) + log, x- 4" O y' = 15e5 ++ 1 - 4* In 4 %3D - I In 2 O y' = 15e5-1 1…

A: We have to differentiate  y = 3e5x + 7 ln(2x) + log2x - 4x.

Q: 3) Show that for any constants M, k, and a, the function k(t – a) y(t) = - M1+tanh 2 satisfies the…

A: Here, the given function is: y(t)=12M1+tanhk(t-a)2...(1)

Q: 1. Express the following as a single log 3log xy-log x +log y a) 6log x b) 3log x c) 6log y d) 3log…

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Q: A logistic initial value problem is given by dP — kP(М — Р), P(0) — Ро. dt M Po i. Show that P(t) Ро…

A: Part (i):   First separate the logistic equation and integrate it by using the partial fraction:…

Q: Find w if w = x10 + 10*. dx 10* 10x° + In 10 log10 e dw dw 10x° + 10* dx dx Option 2 Option 3 In 10…

A: Given  w=x10+10x To find : dwdx

Q: 2 log3 (x) + + log3 (y) is equivalent to: 2 log3 (ry) O log3 (2ry) O log, (2*y) O log, (zy)

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Q: An observation indicates that the frog population Q(t) in a small pond is 25 initially and satisfies…

A: We have to solve given differential equation to find population after t years and then find…