18) Use logarithm properties to comdense each expression to a single log. A) log, (2)+3log, (n) pol B) [In(x)-In(5)] C) log,(x-1)+2log, (x)-log,(x+2)

Q: 91. Prove that log, (x“) and replace x with blog × .) a log, x. (Hint: Start with log, (x“)

A: To prove, logbxa=alogbx

Q: 2. Use BabyStep-GiantStep to compute log;(12) in Zr.

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Q: 9. 8 logx 4. -2 - 3.

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Q: log5 6 is irrational

A: We can prove given result by contradiction method:

Q: log(x) is the exponent to which the base 10 must be raised to get ---Select--- ♥ So we can complete…

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Q: ( logb 16 -     logb 4 ) + ( logb 5 )   ( log3 3 +   log3 6 +  log 3 2 ) – ( log 3 18 )

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Q: 6. Use rules of logs to write as the log of a single quantity. a) 2log3 x - log3 4 b) In x + In(x+1)

A: We will use the listed properties of logarithm to solve this question.

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: Without using the theory of logarithms, show that for any natural number n, there exists a natural…

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Q: Show that 3x2 + log2x2 is Theta(x2). log2x is log base 2 of x.

A: Consider 3x2+log2x2 . It is known that  log2x2<x2, for all x>0. Then, log2x2<3x2 for all…

Q: 8. Use the laws of logarithms to expand In in terms of sums, differences, (cos x)(x +1) and…

A: Some properties of logarith m are :(i) ln(a b) = ln a + ln b(ii) lnab = ln a - lnb(iii) ln ab = b l…

Q: 7) Use properties of Logarithms to write 5logx-log (x3+1) simplity + °aLog (x +1) as 2Log. single…

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

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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: What is the base of the common log, log(x) What is the base of the natural log, In(x)?

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

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Q: 2. Write as a single logarithm with coefficient 1. Simplify as much as possible. Assume the…

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Q: 9.1) How would you compute log(4531.2) using a table with inputs between 1 and 10? Can you explain…

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Q: b). Condense the expression into the log of a single quantity: 3logx + 2logy - logz Ans.

A: Given, The expression 3log x + 2log y -12log z.

Q: 7. If log, w = and log6x + log6 y = 1, then determine the value of log7 (4) + log6 (36x²y²) ?|

A: topic- logarithmic equations logaa=1log(ab)=log(a)+log(b)logab=log(a)=log(b)log(am)=mlog(a)

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: 4. (a) Use logarithm properties to expand In ( (@+5)(x – 6)² (x+ 3)3). (b) Rewrite log3(x) + log3 (y…

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Q: 9.5. Show that (a). Log(1+ i)? = 2L0((1 + i) but (b). Log(-1+i)² + 2Log(-1+ i). %3D

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Q: 5. Use properties of logarithms to contract log 2+5 log x-logy into the log of a single expression.

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Q: 10. Express 17* as a power with a base of 2. log2 log 17 b. 2 4 log 17 log2 d. 2 a. log, 17* c. log,…

A: As we know from the logarithmic property; logaxb=b·logax, where x,a>0 & a≠1   Let, 174=2x…

Q: Expand into a sum and/or difference of logarithms of r, s, and t, or as a single logarithm without…

A: Use the logarithmic identity; logax+logay=logaxy ; where x,y and a>0, and a≠1   The given…

Q: 2. Simplify by writing as a single logarithm: Show all steps clearly including use of 'log' rules.…

A: We have to Answer only Question (2) as stated. We know that,

Q: 5log(8)-1 log(x)

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Q: 4. If log,v =logox- (2logby+log,z), what is the value of v?

A: Logarithm s

Q: 1. Simplify the expression with four a(0,3,4,7,10,12,14).Draw the Circuit in logisim with minimum…

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: Hiw/ prove That: O logi+ 2logi

A: The complex logarithmic function is defined as: log z=ln|z|+i·Arg(z) Where |z| represents the module…

Q: Which of the following in not equivalent to log, 3z O 4 log, y - log, 3x O 4 log, y – log, 3 - log,…

A: logmn=logm+logn log(m/n) =logm-logn

Q: 27a b² Evaluate log, (- V81cd whenever log, (a) = 4, log3 (b) = 0, log, (c) = -1, and %| log3 (d) =…

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Q: 13. Determine whether or not each statement is true or false for all x>0 & y>0; if a false, provide…

A: The solution is :

Q: 13. Determine whether or not each statement is true or false for all x>0 & y> 0; If a statement is…

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Q: Write as the log of a single quanity: 1/2 [3logx + logy - log5]

A: Given that 12[3logx+logy-log5]simplify it in single log quantity

Q: Prove that log(7) is irrational. Hint: Use contradiction and the definition of a logarithm to prove.

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Q: 1. Express logx m + log, n-Glogx m- log, n): as a single logarithm.

A: As per our guidelines we are supposed to answer only one question, kindly repost the remaining…

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: 8. a. Find x if log2x = -2 = -2 b. Find b if log,81 = 4

A: 8. We need to solve the following equations (a) log2x =-2 (b) logb81 = 4

Q: 6. Use log, 10 3.322 and log 8s 0.903 to approximate the value of the expression. log, 100

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Q: Write In 4 + 4 In x + 6 ln (x² + 4) as a single logarithm. Assume all arguments represent positive…

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Q: Prove that log46 is irrational

A: We have to show that log46 is irrational. We are going to prove this by using contradiction method.…

Q: 6. Expand In a*b² as a sum, difference; and/or constant multiple of logarithms.

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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: Let X-N(0,1); show that X member in exponential family.

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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: 2) Use laws of logarithms to fully expand the expression. log9 x²+9.

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Q: 4. The expression loga is equivalent to 5 O 3log.y +log, -log,5 O 3logay +2logax – loga5 | Olog (3y)…

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