20) Solve for x: log(3x + 7) + log(r – 2) = 1 (a) ! (b) 3, - (c) 2 (d) 2, - (c) None of these

Q: ,2,3 Expand into several logarithms: x'y In 25

A: Logarithm is inverse of exponentiations. A logarithm is easy method to express large number and to…

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

A:

Q: Find the value of x satisfying log,, (2×+x– 41)=x (1 – log1,5).

A: It is given that, log10(2x+x-41)=x(1-log105)   Here logarithmic properties are going to be useful to…

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: How do I write the exponential function in the form f(t) = ab^t passing through points (-1, 2/5) and…

A: The solution of given problem is followed by

Q: 5. Show that --I+#^) log, (V +1- x) + log, (VF+1+x) = 0 x². x² + 1 + x

A: We know the property of logarithm, logb(a)+logb(c)=logb(ac)

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: Express th equation in exponential form.

A:

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

A: We make the coefficient 2, exponent inside the log.  And for 1 we replace it by log22 because…

Q: Express th equation in exponential form.

A: a). Given, lnx+1=2 The exponential form is, x+1=e2         ∵lnx=y⇒x=ey⇒x=e2-1

Q: If k is a positive constant, show that x^2 e^-kx approaches 0 as x --> ∞.

A: Given  The x2e-kx approaches 0 as x→∞.Where k is a positive constant .

Q: 4) 19-17-log₂ (2x+4)

A:

Q: 4 Evaluate (logyx)'., having given, 1 1 y = log1,x + ; log,0x + log10x + . 00 1+3+5+ ..+ (2y - 1) 20…

A: We have to solve given problem:

Q: 1 [log, (x- y) - log; (x+ y)]

A: Given that: 12log5(x2-y2)-log5(x+y)

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

A:

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

A:

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

A: Given that Nt represents the number of people who are exposed to a particular advertisement. The…

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

A:

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: 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: 7. If log,w= and log; x+logs y=1 , then what is the value of 13 w3D 7 log, +log, 36x y ?

A:

Q: 8. Let a be a positive real number not equal to 1. Determine the solution of the equation log, (2x +…

A: To determine the solution of the given equation.

Q: 7. Solve for x using log properties: log(5x) – log(x² - 2) = 1 |

A:

Q: 2. Evaluate [log(-1-1)(-2-j2)] tan(4 + 3i) cosh-

A:

Q: 19) 3 log x + - log y - log z

A:

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…

A:

Q: Find all positive values of 'a' for which the equation log (ax) = 2 log (x + 1) has the unique root.

A:

Q: 1. Given that z=8-6i, write its exponential form. Round off decimal answers up to 3 decimal places.

A: Here, a=8b=6

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)"

A:

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: 1. Solve for both the -3 ln (x + 5) - 2

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: Suppose that P0 is invested in a savings account where interest is compounded continuously at 3.1%…

A:

Q: 6) Given that x = log, b. write down an %3D expression for b in terms of a and x. log, t that log, t…

A:

Q: Express log(x²-x-12) - log(x² - 7x + 12) as a single logarithm. State any restrictions on the…

A: Given : expression  logx2-x-12-logx2-7x-12 Prerequisite : Here we use the formula log a - log b =log…

Q: Find the equation of an exponential function of the form f(x) = a · bº that passes through the…

A:

Q: 5. Find y' and y". In x (1) f(x)= (2) f(x)= log,o * 6. Find y' if y=In(x²+y?)

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: (b) Show that 1 1+ 2 tanh- (2) = ; log

A:

Q: 6) If u = log (x² + y²), then prove that log (x² CSScanned with CamScanner dydx ôxôy

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: 2. Evaluate [log(-1-/)(-2- j2)] tan(4 + 3i) cosh-1

A:

Q: Express th equation in exponential form.

A: (a) Given expression is log35=x. Express the above equation in exponential. logab=c, then…

Q: 4 If log3 (x + 1) – log3x = 2, then x equals: F - - 8. 6. G H 8. | 15

A:

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

A:

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

A: We have to prove the result.

Q: Suppose an Egyptian mummy is discovered in which the amount of carbon-14 present is only about…

A:

Q: 3. Solve the natural logarithmic equation. 3 In In x + In In 2 = 4

A:

Q: 7. If the equation 3(5)“ =k is solved for x in terms of k, the result is 1 k (1) x=-log, 3 3 = 2…

A: Solving this expression we have

Q: 13 1. Solve 2 log, (x + 4) – log2 ( 2.x + 2 = 1 -

A: Given,2log2x+4-log22x+132=1 Used Properties: 1. logaxy=ylogax                            Power…