Find the exact value of the expression. (a) 10log(81) (b) In(e4) (c) log3(y 27) (d) log2(40) - log2(5) (e) log27(9) (f) log6(4) + log6(9)

Q: 18. Find the domain and range of g(x) log2(x+3).

A: Domain of log is always greater than 0 .

Q: 14. Solve the equation: log3 (x + 1) + log;(2r – 3) = log, 9

A:

Q: 15. Solve for x: log3 x + log3 (x + 6) = 3

A: To find: The value of x. Given: The equation is log3x+log3x+6=3. Formula used: Product rule of…

Q: 4 log 4(x + 4) -p- X+4

A: Given: ∫04log4x+4x+4dx

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

A:

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

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

Q: Solve the equation.

A: Given, log3x-2=log327-log3x-4-5log51 solve the equation log3x-2+log3x-4=log333-1…

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) Find the value of log (-3 – 3i).

A: you can clearly understand if you follow the below solution

Q: 3. Solve the equation for x a) 45-4x = 1 86-2x b) log2 (2x+4)= 4 c) enx = 11

A: in each part we need to solve the equation for x

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

A:

Q: solve for x: log3 (9)^-1= x+7 note:logarithm is to the base of 3

A:

Q: solve for x in log2 (x+3) + log2 (x-1) = log2 12

A: Givenlog2 (x+3) + log2 (x-1) = log2 12

Q: logx +log(x+3)=1 ? what is x?

A:

Q: 3. Solve the equation for x a) 45-4x 1 = 86-2x b) log2 (2x+4)=4 c) enx=11

A:

Q: #11

A:

Q: 49. log2 x > 3 - 3

A:

Q: 9. Simplify. State any restrictions on variables. log (x²-x-6) - log (2x-6) [K-3]

A:

Q: 10) Solve for x. log5 x - log (x - 2) = log 2 |

A:

Q: 2. Solve for x. (Just type the value.) log (25x + 500) = 3 %3D

A: By simply take exponential on both sides we can solve the given problem

Q: What will the coefficient (x – 1)² in the expansion of loge x about x = 1 ? %3D

A: Introduction :

Q: Solve for x in terms of k. log; a – log3 (x + 9) = log3 k. %3D - x = 1 Find æ if k = 3

A: Use property of logarithms to solve

Q: 5. (a) Solve for x, if log1o(10x + 20)- log10(2x-6) = 1 (b) Given that log10 7 = 1.473, find without…

A:

Q: 25. Solve for x if log 3x = -2. А. 1 В. 1 C. -9 D. -6

A: Our Aim is to solve for x if log3(x)=-2 -(i)

Q: Log4(x2+8) using base e

A: Given  The logarithmic expression is Log4(x2+8) Change of base formula for log

Q: Find the domain of the function. f(x) = 3 - 2 log4 (x/2 - 5)

A: Given function is: f(x) = 3 - 2 log4 (x/2 - 5) We have to find the domain of this function.

Q: 25. Solve for x if log 3x = -2. A. 1 9. B. -9 С. 1 D. -6

A:

Q: How is the logarithmic function (x) = log2(x) related to the exponential function g(x) = 2×? The…

A: Given, fx = log2x gx = 2x

Q: 9 log, x = 2 4

A:

Q: -5- log6(n) + 12 = 7

A:

Q: 3. Solve forx: log x + log (2x/5) -6

A:

Q: Solve for x. 3-2 = 15 O x = log153-2 O x = log 15+2 O x = log3 15 +2 x= log3 15 - 2

A:

Q: 5 log, (p + 1) +2 = -8

A:

Q: Q2: Solve the Logarithms Equation. sin log2(3 - X) - log2 1 + log2(x + 7) 5-x

A: To solve the logarithm equation: log23-x-log2sin3π45-x=12+log2x+7 Solution:   Property of logarithm…

Q: a. Graph Y1 = log |x| and Y, = -log r². How are the graphs related? b. Show algebraically that -log…

A:

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: Exponential 1.f (x) = 23x-6, when x = -1 3x+2 .1 2.f (x) = (-) x-7, when x = 2 Logarithmic 3.f (x) =…

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: 7. Solve the equation. log2(x + 2) – log2(x + 4) = log2(x- 3)

A: To solve log2 (x + 2) - log2 (x + 4) = log2 (x - 3) We use the following property of logarithm…

Q: Solve for xx in terms of k. log3x+log3(x+6)=k x= Find x if k=7

A:

Q: (b) Find the value of x: log ; x - log ; Vx = log 9- log ; 3

A: Basic concepts: remember these properties:

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

A:

Q: Solve for x in log4 (x+1) + log4 (x-1) = log4 15

A:

Q: 7. logaM^r = __________. 8. If logax= loga6, then x = __________. 9. logaMN= __________. 10. True…

A:

Q: Find a formula for the exponential function f(x) = Ca² passing through the points (2,75) 3 (-1, ³).…

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Q: Solve for x in terms of k. log4x−log4(x+6)=log4k A) x= B)Find x if k=1/8

A:

Q: 2. Solve for x: log, (x² + 8x- 20)–log, (x-2) =2 Ans 2 x=.

A:

Q: Q2: Solve the Logarithms Equation. sin log2(3 – X) – logz 1 + log2(x +7) 5-x

A:

Q: 13. Solve for x. log₂ (2x + 3) = 2 log₂ (x)

A:

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

A: Given as