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

Q: Toge Logins 9. 9. 2) loqy(61x VE4")+ log, 4'÷ 256

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want…

Q: PROVE that log, 100 = 2(1 +log; 2)

A: We have to prove that                                     log5100=21+log52

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

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Q: Express In(1+r²) +In r- In sin r as a singel logarithm.

A: Use property of log :→n ln(m) = ln(mn)→ln(m) + ln(n) = ln(mn)→ln(m) - ln(n) = lnmn

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

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Q: 44. Express as a single logarithm and simplify: In(x10)-In(y20)

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Q: The logarithmic expressi on In can be rewritten as (1) 3ln y- 2 In y- 6 (3) 2 1-6 In y (2) 2 (4) Vin…

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Q: log5 6 is irrational

A: We can prove given result by contradiction method:

Q: (*) We can expand log to get

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Q: 2 Solve log, (2 sinx) + log,(cosx) =-1, for 2n<x<-

A: According to Bartleby's guidelines. We are allowed to solve only 1 question ata time. Apologies for…

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: 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: 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: Expand: log, (xVy).

A: logbxy3=logbx·y13

Q: Express in terms of logarithms of x, y, z, or w.

A: Given logarithmic expression is log4xz. To express logarithms in terms of x, y, z or w. Solution: We…

Q: 9. Between what two consecutive integérs must the value of log,s00) lie? Justify your answer. gol-v

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Q: determine the nature of functon for even and odd Ax) = log(x+ Vx² +1) ?+1)

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Q: If x2 + y2 = 25xy . Then prove that 2 log(x+y) = 3log3 +logx + logy

A: It is given that x2+y2=25xy add 2xy to both sides  x2+y2+2xy=25xy+2xy using the formula…

Q: 101. Show that log,(x + V – 1) + log.(x - Vr - 1) = 0.

A: To show: loga(x+x2-1)+loga(x-x2-1)=0 Solution: loga(x+x2-1)+loga(x-x2-1)=0 Considering, Left Hand…

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

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Q: What is the value of x in logx > 2log4?

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

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Q: Expand In (rs" Vr*s into a sum or difference of logarithms containing no exponents. > Next Question

A: Consider lnr8s7 r4s36

Q: Express as a single logarithm. (a) į In x- 2 In(x' + 1) (b) In(x – 3) + In(x + 3) – 2 In(x² – 9)

A: "Since you have posted multiple questions, we will answer the first question.  If you want the…

Q: Use rules of logs to write the log as a single quantity 2log3x - log34     ln x + ln(x+1)

A: GIvenA)2log3x-log34 B) ln x+ ln (x+1)we have to use rules of log to write log as single quantity

Q: Prove log, + log, 20 log, 8 = o

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Q: Suppose that a and y are real numbers such that log2 (x) = – 3 and log2 (y) 6. Calculate the…

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Q: Evaluate the limit as x approaches infinity of log7x/log8x

A: We need to evaluate the given limit

Q: Show that J log(1 + tan0)d= log2

A: Given that: To prove:        ∫0π4log(1+tanθ)dθ=π4.log2

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: Between which two consecutive integers must log, (40) lie? Be sure to explain your reasoning. //…

A: We have the given number as log340 Let us consider that, 33&lt;40&lt;34

Q: -, State the transformations that are needed to turn y 4 log10(x – 4) into y = – 2 log10(x + 1).

A: Compare the both equation and take transformation and varify

Q: fin log In () (2)In

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Q: Solve for all valid x: 2log(x) = 1+ log(x+ 1) Attach File

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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&gt;0 &amp; a≠1   Let, 174=2x…

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

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

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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: 10. Express as a single logarithm. 6 log x + log 10 - log(x + 2)

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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: ,162,20 If log A log(x) + Blog(y) + C log(z) 27 A = В - C =

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Q: 2. Rewrite as a single log (condense): 7 5, loga (xy®) +12lo9 x12 - 5log. (y) 16,,8 8

A: Answer and explanation is given below

Q: Evaluate y for the fx)= 4"-5 log,(x) 4*ln 4- Inx 4- x In 9 4- In 9 4'ln 4- x In 9

A: Answer

Q: what is intergral log x /x

A: WE HAVE TO INTEGRATE

Q: Assume X, Y, Z are positive numbers. Use propertie of logs to write the expression - 2log X-blog₂ y…

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Q: Without using log tables prove that 1orsid ei boeu ss to 16 +12 log10 15 25 +7 log10 24 81 = 1 80…

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Q: Write out a table of discrete logarithms modulo 17 with respect to the primitive root 3.

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Q: Evaluate So ·∙log 1+ax 1-ax (: ( dx x√√1-x²

A: A very good problem. This problem illustrates the power of differentiating under the integral sign.…

Q: Express single logarithm: log; x + 2 log, y – 3 log; z as a

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