ii) 2 log, (x)– log2 (3x – 4) = log, (x – 1) – 1

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: 1) 2-log₂ y = 2log₂ (x+y) log₂ (x+y)+ log₂ (x² − xy + y²)=1

A: We have to solve given problems:

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

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Q: (ii).Given that log, (y-1)+log, = z and log, (y+1)+log, x= z – 1, Show that y = 1+8° and find the…

A: Given: log4y-1+log4x2=zlog2y+1-log2x=z-1 . . . . . (equation 2) Concept: Here we shall use the…

Q: 8. In V5x 3 y z2 9. log. V xt 10. loga Va b5

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Q: 11-e18 x x+log3¤ Find y' where y =

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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: 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: f (x) = sec(3x – 1) * log3(2 +x) -

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Q: 3. Use Log Rule to integrate. a. Sor5 Sdx а. бх-5 b. S; -dx x(lnx)²

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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: 2. Differentiate: a) y = log2(3x) %3D 2 b) f(x) = –7 log(x²) %3D

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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: 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: #11

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Q: woubnat Solve for x 7* = 12 a. b. log(x+5)+log(x-4)=1 c. log, (x+3)-log, x= log, 7 %3D d.…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 4. Determine the co-ordinates of the point of intersection of the graphs of f(x) = 5(3*) %3D log a…

A: The given curves are  f(x) = 5.3x f(x) = 7.2x

Q: 1. Find the value of y. a. log;25 y b. logy32 = 5 c. log,y

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

A: We will prove the following result.

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

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Q: (b) 5" (2 – cot 5")(1 – csc 5“) dx SC 11 – 2 log x (c) / dx JIV6 log r – logʻ 1 x/6 log x -

A: You have asked Only part b and c

Q: 14. Find the domain of definition of the function 31 Vx + 5 X-5 y = log10 (,2 x² – 10x +24

A: The domain of a function is the set of input or argument values for which the function is real and…

Q: Q3\ Solve for x: a. log(20x + 1) – log(x – 2) = 2 b. In(x - 2) + 2 in Vx+ 3 In6 %3D

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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: 7. log;(x²) =, x log5(_ 8. log,(y*) = x log-(. 9. log(V1000) = – x log( %3D

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

A: on applying log algorithm we will get

Q: Solve for x. (a) In (x – 3) = 7 (b) In (x + 4) + In (x - 4) = 1 (c) log gx² - log ,2x = 3

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

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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: 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: x-1 X-n x+n If y = x log show that y, =(- 1)" - 2 (n – 2) ! %3D x+1 (x - 1)" (x + 1)"

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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: 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: 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: Solution to the equation Log(2iz + 1) = in is None of them z = ni z = i

A: Usually, log x is represented as log10x . If log x=y , then x=10y .  The natural logarithm, ln x is…

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: 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: 7. Find y'. y = log, (9– x-x)

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Q: rewrite each expression as a singlelogarithm.

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

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

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Q: 12. Evaluate a) xcos2x dx, leaving your answer in terms of n. b) dxusing the substitution u 3x + 4…

A: Integration.

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–…

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