1) f(x) = Vx- 3+ V5-x 2) f(x) = /3 – log2 x2- (log2 x)² %3D %3D

Q: 2. Ifƒ (x, y) = log (x² + y²), then ƒ +ƒ is equal to XX yy 1 (a) x² + y² (b) 0 1,² - x² (c) (d) *…

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Q: Solve x*+6r34y dx+ +3x=+y = (1 + logx)* dx²

A: Given differential equation, x4d4ydx4+6x3d3ydx3+9x2d2ydx2+3xdydx+y=1+logx2 This is a homogeneous…

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

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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: log. (2-1)-log. (x-u)= 2 log Cao) (x-4)=

A: Use the following properties of the logarithmic functions, while solving this equation. log a - log…

Q: 7. f(x) = 6e* + log2(7x² + 3x + 1) f'(x) =

A: Given: fx=6ex+log27x2+3x+1 Differentiating fx with respect to x, f'x=ddx6ex+log27x2+3x+1…

Q: 1. y = v4x + 3 log2(x² + 2) 2. y = 3vx²–3x+1

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Q: The solution to log₃(log₂x) = 1 , is:   A. x=4 B. x=8 C. x=1 D. x=2

A: Formula: If logab =c  Then b=ac

Q: f (x) = sec(3x – 1) * log3(2 +x) -

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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: 4) 19-17-log₂ (2x+4)

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Q: (22x + 2) dx 11 In|x² +4] +2 tan -1 x2 + 4 +C 2 Logarithm function is missing parentheses around its…

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Q: 10- 11- 12- In 2 log₂x X 2 log10 (x + 1) x + 1 dx x log10 x 0 S -dx -dx

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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: 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: 1) x³+ 2x - 2y = x² logx + x dx3

A: Since you've asked multiple questions, as per the answering guidelines we are supposed to answer the…

Q: (1) Solve the following: (a) 42x-1 = 64 (d) In 3 – In x – In(x + 5) = 0 (b) 81–x = 4x+2 (c) 22x + 2×…

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Q: 3. Solve the following equations for x: (a) 3*4*+2 = 8 (d) log₂x = 2 (b) 3 lnx + 2 ln x² = 6 (e)…

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Q: [ Зх +1 x – 3 A 3x + log (x- 3) 3x + 10log (x- 3) в Зх + log. (x- 3) +с 3x + 10log (x – 3) + c

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Q: solve for x in the following equation 2e^3x-1=10

A: To solve the equation

Q: 1.Solve by logarithmic differentiation -(x+1)(x+2)(x+3)2 Y=In(- V(x+3)3 (x+4)*

A:

Q: 4. g(x) = 4x³ log, X 5. f(x) = 10* · e* 2x-x2 logze e²10* c. e*10* + loge e*(x-3) x²-4x+4 e. 4x²(3…

A: "Since you have posted a two questions, we will solve first question for you. To get another…

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: 12. f(x) = 3* %3D 15. f(x) = %3D 18. f(x) = log3X

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Q: 2. If the rate of transmission of an additional case of covid-19 is 0.3 per day starting February…

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Q: 1. y = e9z-5 2. y = 2x ln(x +2) 3. y = (2x – 5) log(3x² – 6æ)

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Q: 2 Solve (x²D² - xD + 4) y = x² sin (log x).

A: Given differential equation is x2D2−xD+4y=x2sinlogx. We have to find the general solution of the…

Q: 1 5 log5 (x) + log5 (y) - 6 log5(z) 6

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Q: 2. 18|ャ 2. 1. 1. 1. 1. y= 2 log2 x 1/4

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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…

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Q: In (x + 4) + x = 5 log log (x + 1) +3

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Q: 2. Solve for x. 45x-x² = 4-6 a. b. (1 − x)5 = (2x − 1)5 - 60 c. 55 = 1+5e-0.6x d. 3 log x + 10 =…

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Q: 5. ƒ(x) = 10* . ex 2x-x2 a. 2 b. logze e 10 c. e*10* + loge e*(x-3) d. x²-4x+4 e. 4x²(3 log, x +…

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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: 7. Differentiate y = log10 (x² + 1)² b. 4xlog10e x²+1 a. 4x(x² + 1) c. log e(x) (x² + 1) d. 2x(x² +…

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Q: 9) Solve for x and y in the following pair of simultaneous equations log (x+ y) = %3; 2 log x = log…

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Q: - f(x) = - f(x) = x-2 g(x) = 5 In x - 2* g(x) = 4x' log, x %3D f(x) = 10* · e*

A: Solution of question is written in below steps.

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: Suppose a certain population is initially absent from a certain area but begins migrating there at a…

A: Consider the provided question, Suppose a certain population is initially absent from a certain area…

Q: What is the simplified form of 4 * log_3(y) - 6 * log_3(x) + 7 * log_3(z) ?

A: Find the simplified form

Q: 13. 3*-5 -4 14. In(x – 2) = 4 %3D 15. log(x + 9) + ipgx = 1

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Q: 4. y = log(x² – 7) 5. y = ln х+2 x-3 31

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Q: It is expected in traditional mathematics that when you input data into a well-defined equation you…

A: As per the question we are given the logistic equation : xn+1 = f(xn) = rxn(1-xn) And we have to…

Q: 4. Solve for x: a. 100(1.04)²x = 300 b. 2+ log v1+ x + 3 log VT–x = log v1 – x² c. V35x-I = 9 d.…

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Q: 4 In2 log2 x 1-

A: At first we will change base of log2x to natural log by using base change formula. Then use…

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: Differentiate : a. y=log2√x b. y= 2x^(3x) c. y = (x+1)^x

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

A: topic - derivative of a function

Q: Solve for x (to four decimal places) in each of the following: (0.26) log25) (4x- f) (414)x (1/4)*+3…

A: (f) The given expression is,

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.