(a) x² – x = log, 25 (b) 3x + 5 = log, 64

Q: Show that -b + VE - 4ac log -b - VE - 4ac + log 2a 2a = log e - log a

A: We have to show that,  log-b+b2-4ac2a+log-b-b2-4ac2a=logc-loga

Q: 2 Find x so that log10 x = log, 10

A:

Q: log10(2x- 4) = 1+ log10 4, then 'x' is equal to ...............

A: We have to find x

Q: Differentiate. a) y=log2(3x) b) f(x)= -7 log(x2) c) g(x)= x6log(-4x) d) h(x)= log8(2x4-3x)

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

Q: (b) For what value of x is log₂ (x+1)-log₂ (x-1)=3?

A:

Q: -16 (ii) log,(x– 2)+log,(x) =1 32

A:

Q: 4x³ (log3 x)" (csc5 x) Vsinh(2x – 8) b. y =

A: We differentiate the given function using quotient rule of Differentiation i . e .  If   y ( x  ) =…

Q: log2(7x+2)=2, then x=

A: Given:- log2(7x+2)=2,  To find:- Value x

Q: 3x = 76x-5 d. log2(x+30) + log2x = 6 e. 2x^2 = 162x-3

A:

Q: Solve for x: log3x + log3 (x-8) = 2 + 8log51 and 2x - 15 is a.) -4  b.) 3  c.) 2  d.) 5  e.) 8

A: To solve

Q: b) f(x) = -log2(2x + 3) – 3

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: 23. Solve for x: a) log, (x- 5) + log,(x - 2) = 2 b) 5*+2 - --2500

A:

Q: If  x is an integer then solve (log2x)2-logx4 - 32 = 0

A: The given equation is (log2x) 2 -logx4 - 32 = 0

Q: If log3 (x)=4, log3(y)=-1, and log3(z)=5, what is log3 (xy)? ?

A: Objective of the question find the value of expression with the help of given data.

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

A:

Q: i) log, (5x + 4) – log,(4x) = 2. ii) 9e* + 4e-x – 12 = 0.

A:

Q: Express as a single logarithm   In x2 -2x-24/x-2-In X2 +2x-8/x+9 + In(X2 -12x+36),  x>0

A:

Q: 4. Find the domain of the log function. y = In((7 – x)(x + 10)) Use a sign chart.

A:

Q: * (x-9) log2 y

A: Since, you have asked multiple questions in a single request, we would be answering only the first…

Q: Express as a single logarithm   In x2 -2x-24/x-2-In X2 +2x-8/x+9+ In(X2 -12x+36),  x>0

A:

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

A:

Q: x² 6 + ,X log (x² + 7)(x³ – 5)² -

A: Laws of Logarithm:

Q: log(3-x) = -1

A:

Q: log (x2) - log(v9) + log(z4) condensed into a single logarithm is expressed as log() Select one: O…

A: Expression is given by logx2 - logy + logz4 To evaluate : Single logarithmic expression.

Q: 3. Express as a single logarithm: 3 log 2 + log x - log (4x) log(8x) A. log(4x) В. log (2) C. log…

A:

Q: 3. 9. a) Solve for x: log4 xX = b Write as a single log: 2log, 3x + 3log5y – 4log5z

A:

Q: (2) Combine the following into one single logarithm with a coefficient of 1 in front of the entire…

A: 6log4x-5-34logx+log9x-1

Q: a. f(x) = ln 3sqrt(2x^3+5) (Use log properties to simplify first)

A: Solve the following

Q: Solve:  A) log (x + 9) – log x = 1 B) log x + log (x – 3) = 1

A:

Q: A: 2e2x-5ex-3=0 B: log3(x2-6x)=3

A: (A) Given equation is: 2e2x-5ex-3=0 Let us consider, ex=u Then we get,…

Q: B. Convert to an exponential equation. 1. log, T =x 2. t= log, 7 3. In 0.38 =- 0.9676 5. log 0.01 =-…

A:

Q: log, x+ 2) <0

A:

Q: (а) е" =D1 %3D (b) log(x – 3) + log(x - 6) =

A: Given that: (a)ex2-9=1(b)log(x-3)+log(x-6)=1

Q: Given 2 log3(x + y) = 2 + log3x + log3 y, show that x² + y² = 7xy.

A:

Q: a) 4 – 113x-2 = -23 %3D b) log, x + log6(x + 1) = 1

A: Please refer the attached image for complete solution.

Q: 9 log, x = 2 4

A:

Q: Suppose log, 3 = 15 and log, 5 = 22, find: %3D a) log. 9 b) loga 75

A:

Q: The exponential form of log(x)+log(y)=-2 is: x-y=10^-2 10^xy=-2 x+y=10^-2 xy=10^-2

A: This question is related to exponential and logarithmic equations, we will solve it using given…

Q: 3. Solve for x: log, (x+6)- log,(x-2) = 2 4. Solve for x: log, (x-5)+log,(x+1) = 4

A:

Q: log/ yx-y+3 1-4xt y 4X - log 3 4x ニ

A: Graph

Q: x- log, (x – 6) = log , 9 4) log, (x– 10) + log, 4 = 3 %3D g7 g, (x + 3) – log, x = 1 6) log, 8 +…

A:

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

A: An equation is a formula that provides the equality of two expressions, by connecting them with the…

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: 6. Expand the expression 2x+3 log (x+4)°(x- 3)*

A:

Q: 1. solve for x, log2(3x-2)=4.    2. use the laws of logarithims to rewrite 7log x - 3log y as a…

A:

Q: 1. y = -3+log, r 2. y = log, (r – 2) 3. y = - log, (æ + 3) 4. y = 2 + log,

A: we have to match

Q: 5-Solve a) log3x + log3(x + 6) = 3 b) log10 (3x-2) -2log10 X+1 = 2 c) log, (1– x) + log,(2x– 5) = 3…

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

Q: How would you describe log, (2-x) for x=5? Why?

A: Given: log7(2-x)

Q: What are the steps involved in this problem? log (x-10) - log (x-6) = log 2

A: Given as

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.