The value of the expression log325 – log33 – log375 is - a) -3 b) –2 c) 4 d)-4 إختر أحد الخيارات: (d) (c) (a) (b)

Q: How are the two equations 102=100102=100nn and [][]log10(100)=2log10⁡(100)=2 related?

A: We need to show relation between given equation.

Q: If log,3 =z, then log,81 expressed in terms of æ is

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Q: While simplifying the expression log48 + log,7-log,8, shyam got the simplified form as log 48. What…

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Q: 6. Solve log,(1 – 3x) = log,(1 – 5x) – log, 2x (A)

A: Some of the properties of the logarithmic function  If logax=logay then x=y logax+logay=loga(xy)…

Q: log5 6 is irrational

A: We can prove given result by contradiction method:

Q: (ii) log,(x+3)=1–log,(x-1)

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Q: Give at least two examples of the first 3 logarithmic properties.  Property 1- Property 2-…

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Q: Evaluate the expression, log5 1/25 without using a calculator. If evaluation is not possible, state…

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Q: 4. Use the properties of logarithms to expand the expression as a sum, differences, and/or cons…

A: The given expression is logbx5b6y7z164 We expand the expression as sum , difference of logarithm…

Q: Exercises 150-152 will help you prepare for the material covered in the next section. In each…

A: log232On simplifying further we get:log232=log225        (using,25=32)⇒log232=5log22…

Q: solve the Fo llo wing 3) log,el- 2 logs 3 ↑) logiz 12- 2 log 2 2 5) .lo9221 - logz 7

A: This question is based on Logarithmic properties.

Q: Use the Laws of Logarithms to combine the expression. 3 In(2) + 5 In(x) - - In(x + 7)

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Q: Because the equations log(3x + 1) = 5 and log(3x + 1) = log 5 are similar, I solved them using the…

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Q: Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as…

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Q: Because I cannot simplify the expression bm + bn by adding exponents, there is no property for the…

A: The expression bm+bn cannot be simplified by adding exponents, because we add the exponents when we…

Q: Let a = ln2 and b = ln3. Use the log properties to express the value ln72 in terms of a and b.

A: By using logarithmic property, we express the given logarithm.

Q: asb b? =In 2. %3D (3

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Q: jlog(4- ji') (541.5) In log(4ejn) j log(-7)

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Q: Express th equation in exponential form.

A: (a) Given equation log515=-1 Use the basic rules for logarithms, if logbc=k, then solution of this…

Q: Using logarithmic properties, what is the solution to log4(y – 9) + log43 = log481? Show all…

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Q: 4. Rewrite log(AB²) in terms of logA and logB, or state that this is not possible. log(AB?) = ,

A: We will solve the logarithm problem.

Q: PROVE that log5 100 = 2(1 + log5 2)

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Q: In Exercises 23-25, write each expression as a single logarithm. 23. 8 log, x log, y 24. 7 logs x +…

A: The given expression is 8log7x-13log7y

Q: 1. What is log,, 100? What about log,00 10? 2. What is log, 4? What about log, 2? 3. Express b as a…

A: values=?

Q: 4. If log, 2(x + 6) =log, 36, then the value æ is 5. If log, æ = 0.5 and log, y = 1.16, then the…

A: We have to solve given logarithm equations. In the first equation we have to find the value of x.…

Q: What is the real part of Log(-5 + 51)²? What is the value of Log(-5+ 54)? – 2Log(-5+54)?

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Q: ( 3vx log9 x²+9,

A: The expression is  log9 3xx2+9

Q: Evaluate the expression log3(log8 8) without using a calculator. If evaluation is not possible,…

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Q: Express th equation in exponential form.

A: Part (a) - log381 = 481 = 34                                If logba = c, then a = bcHence,34 = 81

Q: 1 Use log,4 0.712 and log. 12~1.277 to evaluate log, 3 1. log,

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Q: .Express in index notation: a) loga 8 = c ii. Simplify: 3log3 - log 27

A: I.Express in index notation:  a) loga 8 = cAnswerlogam=n ⇒ m=anThereforeloga8 = c ⇒8=ac

Q: I estimate that log8 16 lies between 1 and 2 because 81 = 8 and 82 = 64.Determine whether the…

A: Given information: The value of log816 lies between 1 and 2, because 81 = 8 and 82 = 64.

Q: 8) Solve the equation log, (x + 3) = log,(2x

A: We will solve for x.

Q: Simplify log, (x+ 4) – log, (a- 5) O log, 9 O log, (2x - 1) z+ 4 log4 I- 5 log, (2-z- 20) 2--20)

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Q: A login for a bank website consists of 2 letters followed by 5 numbers.  If only the letter cannot…

A: Given- A login for a bank website consists of 2 letters followed by 5 numbers. To find- If only the…

Q: What can you conclude about log2 16, or log2(32/2)?

A: The given function is log216 or log2322 The logarithmic property is expressed as log mn=n log m The…

Q: if m=log10 n, what other relationship exists between m, 10, and n?

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Q: Evaluate the expression log3(log2 1/8) without using a calculator. If evaluation is not possible,…

A: Evaluate the expression log3(log2 1/8) without using a calculator. If the evaluation is not…

Q: Solve : log, (26 – x) = 3 log, 6 - 703 242 755 -190 190

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Q: Evaluate the expression log2 8 + log5 25 without using a calculator. If evaluation is not possible,…

A: Given expression: log28+log525

Q: 7. Solve. log, (x-6)+ log, (x-5)=1

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Q: Show that, log(-1+i)² # 2log(-1+i).

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

Q: Express log,(9AB) in terms of log ,4 and log, Bin simplest form.

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Q: Which statement is true? 4 is a solution of 25x +3 > 73- O 4 is a solution of logx + 2 < 2. O The…

A: We have to check

Q: Oloo. log12 D-

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Q: Prove that log3(25) is irrational.

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Q: 5. Determine an expression in terms of x, y and whole numbers for log, 400 if log 980A

A: Introduction: We will use some logarithmic properties to solve this problem. log(mn)=log(m)+log(n)…

Q: Express th equation in exponential form.

A: To express the given equations in exponential form: a)log5(1125)=-3,b)log84=23 Solution: We know,…

Q: log, n - Glog, m – log, n) as a single logarithm. 4 1. Express- log, m + logx n) as a single…

A: We have to convert the following into a simple logarithm form -  34logxm + 23logxn - 12logxm -…

Q: Find a formula for the exponential function passing through the points (-3, 6250) and (2, 2) f(x) =…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.