93. Use the results of the two exericses above to prove that: (a) log,(÷) = - log, x (b) log,(÷) = log, x – log, y

Q: Suppose that log, x = 5 and log, y = 4 compute %3| log, Vx²y³

A: Given

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…

A:

Q: (*) We can expand log to get

A:

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

A:

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: 120 FIK)T log, =x, express log in terms of x

A:

Q: If log,b = x³ and log,(÷), determine the value of x by showing all steps in using the appropriate…

A: logab=x3b=ax3

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: 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: log,,3 + log, (4x + 1) = log,o (x +1) +1

A:

Q: Express in terms of sums and differences of logarithms. 8 In 3xy 8 In 3 3x°y

A:

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: The union of left ray topo log y and right ray top log y on real numbers is usual topo log y True…

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

A:

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: 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: 2 1. Express log,(64 x v64*) + log, (46 V256. 43 logarithm

A: Using log44 = 1

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

A:

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

A:

Q: If log (x³ (x-2)) is expanded to Mlogx+ Mog(x-2, what 3 thhe sum of Mand N?

A:

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: 4 In x + In(x - 25) is the base e logarithm of

A: solution:-

Q: 7. If log,w= and log; x+logs y=1 , then what is the value of 13 w3D 7 log, +log, 36x y ?

A:

Q: If log base b (x)=0.35 and log base b (z)=0.85. Evaluate the expression of log base b (square root…

A: We have given and we need to evaluate :

Q: 729 Given that log, 2+ log, 3 =1, express log, 1024 2187 and log, 2048 (i) in terms of log, 2 only.…

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Q: If VA= B, then log a B =. --

A:

Q: 11. If Log(3) = 0.4771 and Log(2)=0.3010, compute Log(√3456) without using a calculator.

A: Given:-log(3)=0.4771log(2)=0.3010using properties of loglog mn=nlogmlogm·n=logm+logn

Q: Find all vawes of k don uhich log kx 112 log (x+) has one soluhion

A: Just use basics of logarithm.

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

A: Logarithm s

Q: Given that x, y, z >1 and w be a positive number such that log, w = 24, log, w = 40 and logrvz W =…

A:

Q: -Given that p log, 5, q log, 2 express the following in terms of p and/or q. log, 0.625

A:

Q: pressions without using a b) log, (log, 125) d) (log, 128)(log4 256) f) log, 82 – log, 49 + log, 1…

A: We have to solve the logarithmic expression.   According to our guidelines we can solve only three…

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: 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: 6) Given that x = log, b. write down an %3D expression for b in terms of a and x. log, t that log, t…

A:

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

A:

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

A:

Q: Express the following in terms of x without logs or natural logs 1) log100x 2) 1000logx 3)…

A:

Q: 9. Express equivalent expression: log(x – 3) – log() + log 4 as an x+3

A:

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: If (5)** = 16 and log x-y8 =- 3, calculate the values of x and y. %3D

A: lna(b)=y then b=ay  (am)n=amn

Q: Express p in term of q if: log,p -log,q =1

A: We have to express p in terms of q.

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.

A:

Q: Show that if log, a=c and log_ b = c, then log, y =c².

A: Using the properties of the logarithmic functions, it an be written that logbc=log clog b.  Using…

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: The union of two topo log ies is topo log y True O False O

A:

Q: 3-Given that a=log, 3 and b=log ,6, find log, 24 in terms of and b

A:

Q: 2 log, 64|,B = |** 6 [x +3 = 4 В 10 -4] 4 [m LetA = 4 21 3. 2 -7 5 4 and D =, *,. Find X, if AB" +…

A: To find the value of X.