8. Let a be a positive real number not equal to 1. Determine the solution of the equation log, (2x + 3) = log, (5 – x) - 2. %3D

Q: (a) log,(5x – 1) + 6 = 9 (b) 163x+1 = (4)*-1 %3D (c) In(x + 6) = In(11) – In(x – 4)

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Q: m=4 , n=5 2 log, 641.B = <+3 = 4 10 1.c=* 2. LetA = 4 4 21 т -7 and D = -1 Find X, if ABT +…

A: Two matrices A=a1a2a3a4 and B=b1b2b3b4 can be multiplied using the rules of matrix multiplication.…

Q: (1) (a) Solve the following: 1 (i) 2*-6 8 (ii) log, (x+3) =1– log, (x-1) = -

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Q: The number N(t) of people in a community who are exposed to a particular advertisement is governed…

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Q: in The solution of the equation Log(z² – 1) = is %3D Select one: 1 in 1 19T 22e 8 and 22e 8 1 in 1…

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Q: y = loga 4x 6.

A: Differentiate with respect to x.

Q: 5. Find y' and y". f(x)= log,0 x Find y' if y=In(x²+y?) 6.

A: f(x) = log10x ∴ f'(x) = 1/x and f"(x) = -(1/x2)

Q: Disprove the statement log(x + y) = log x + log y by, a) Letting y equal a positive constant of your…

A: Given  The statement log(x + y) = log x + log y

Q: 1) Solve for x and y in the following simultaneous equations *a) log, x = 2; 5y= x +12 log, y *b)…

A: We have to solve for x and y in the following simultaneous equations.

Q: A relationship between (y – 2) and (x – 1) is given by (y – 2) = ab(x -1). . With a suitable linear…

A:

Q: 6. If 16 and log,(x – y) = 2, calculate the values of x and y algebraically. 1/2

A: Given,12x+y=16and log8x-y=2

Q: in The solution of the equation Log(z² – 1) = = is Select one: 1 in 1 15n 24e 4 and 24e 4 1 in 1 19n…

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Q: If logy =c- log,x, where y> 0 andx > 0, then y is equal to A. c-X В. 3 D. C.

A: To solve the given logarithm

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: Find graphically approximate value of the root of the equation an 3 – x = e* - 1.

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Q: (1) (a) Solve the following: 1 (i) 2*-6 8. (ii) log,(x+3) =1– log,(x-1)

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

Q: D) log3 (x² – 5) = 2

A: To solve the equation for all real values of x log3(x2-5)=2

Q: 4. Solve the following logarithmic equation: log3 (Z + 8)x7 – log3 (2K + 9)x3 = log3(Z + 5)x2 + 4(Z…

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Q: Solve the following equations: 2 x³ = 49 3*.27*=9 √5*=25(x-1) d. b. log₂ (6x-4)=-1 28=2(5*)

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Q: 11) Given that log, 6= m and log, 5 =n, show that log, 10 = mn+m-1 %3D 12) Solve for x in the…

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Q: 4. Solve the following logarithmic equation: log3 (Z + 8)x7 – log3 (2K + 9)x3 = log3 (Z + 5)x2 + 4(Z…

A: loga(B) + loga(C) = loga(BC) loga(B) - loga(C) = loga(B/C)

Q: 7. Solve for x: 48 = 6e4x b. log (x?) + 3log (x) log (32) а.

A: Given : a) 48=6e4x   b) log(x2) +3logx=log32

Q: 5. Which of the following functions grow faster than In x as x →o? Which grow at the same rate as In…

A: Hey, since there are multiple subparts posted, we will answer the first 3 subparts. If you want any…

Q: 2 log , x + 12log, y

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Q: 4. What is b if (log, x)' :? Зх

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Q: 4. S(x) = log,(-x)

A:

Q: 17. Find the value of x without the use of calculator 1 log, 3. 4

A: Given:

Q: Determine whether the following statements are true and give an explanation or counterexample.

A: Given information:

Q: 7) Propose an equation similar to log 4 + log x = log 27 whose solution is 9 %3D

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Q: 4. Which of the following functions grow faster than x2 as x→∞? Which grow at the same rate as x²?…

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Q: ) for the log equation log(x+1) + log(x-2) =1 The number of solution is ________. The sum of…

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Q: In particular, the law says that the time, T, it takes to make a choice can be modeled by the…

A: Given T = b.log2(n+1)where n = number of options from which to choose,b = constant number T = time

Q: 9

A: We need to solve

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: 8. Let b be a positive real number not equal to 1. Determine the solution of the equation log, (2z –…

A: See the solution step by step.

Q: 4. Solve the following logarithmic equations: a) logx+log(x+15) =2 b) log,(x+1)= 1 +log, x d)…

A: We have to find value of x for given problem

Q: 2 Show that the following functions are harmonic in x and y: 2 log√x² + y²

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Q: 3 Given that xand y are real numbers, x>0, if 4"-3x' 16, log, x=, r+1 y find the value of x

A: Given: x and y are two real numbers, x&gt;0 4x-3xy=16 log2x=x+1y We can write, 4x=16 +3xy⇒2x2=16…

Q: 13. Express the following equations in exponential form. (a) logs 5 = 1 (b) log, Q = k (c) In 30 =…

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Q: 9. Solve the following simultaneous equations: logx+log(y²)=4 log²x-3log(xy)=-5 Where x,y are real…

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Q: (a) f(t) = In(5t - 4) 12 (b) g(x) = log(x² - 25)

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Q: 2. Solve for x, to one decimal place. (b) 7* = 35 %3D (a) log, 56 = x

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Q: (7) (7 pts) Solve the equation. log(x – 2) + log(x+3) = log(6x)

A: Here given as logx-2+logx+3=log6x

Q: 8. Solve. Give EXACT answers only- (a) e**1 = ! %3D (b) 3log2(x – 1) = 5 – log24

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Q: Given that log, x + 2 log4 y = 4, show that xy = 16. Hence solve for x and y in the simultaneous…

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Q: If r (x) = log(x – 3) and s(x) 2 log x, which function represents (r + s)(x) ? |

A: It is given that, rx=logx-3  and  sx=2logxWe have to find the value of r+sx

Q: 2 log, 64|,B = |** 6 [x +3 = 4 В 10 -4] 4 [m LetA = 4 21 3. 2 -7 5 4 and D =, *,. Find X, if AB" +…

A: To find the value of X.

Q: 4. Solve for x , show all work and round off to three decimal places if necessary. a) log 83 = x b)…

A: b) The given equation is log3y=1.69 Use the base theorem, logab=ln bln a. 1.69=ln yln 3ln y=1.69· ln…