The least value of the expression 2log10x – log(0.01), for x > 1, is- (A) 10 (В) 2 (С) -0.01 (D) None of these

Q: Show that loga 12x + 2x - 12 + loga 12x - 2x - 12 = 0.

A: given :                      loga (12x+2x-12) + loga(12x-2x-12) = 0 The product rule for logarithms…

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

A: Given

Q: 5. Suppose that A = Use the definition of the exponential to calculate exp(At) in terms of familiar…

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Q: 3

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Q: log5 6 is irrational

A: We can prove given result by contradiction method:

Q: The simplified form of In(÷-) using logarithmic rule is yz 4ln x+ In y- In z 4 In x- In y-In z 4ln…

A: The objective is to simplify the given expression using logarithmic rule. The given expression is

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

A:

Q: single, simplified logarithm Express as a 1- (log510 + 2log53)

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

A:

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: What is the zero o of the funcHon Y= loge (x+G)-I?

A: Given: The function, y=logxx+6-1.

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

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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: 2. Why is it not necessary to know the value of "a" to determine the value of loga(-1)?

A: Given logarithm, loga(-1)

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: Express -log x+5log y as a single logarithm. (A) log -+5y ® log(Vry³) log(V+ y*) (D) log 2

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Q: Estimate the error in the value log 2.7 obtained from the following dată.

A:

Q: Does the function f(x)= logarithm x with the base of 1/2 approach a certain real number as the value…

A: Given

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

A:

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: 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: 2 -3 r- 3 x = %3D (z + 4)- 1 = 24 --- log, 15625 6 X = !!

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Q: Express irrational solutions in exact form and as a decimal rounded to three decimal places. log16 x…

A: Given logarithmic equation is: log16 x + log4 x + log2 x = 7 We have to solve for x.

Q: Express irrational solutions in exact form and as a decimal rounded to three decimal places. log2…

A: Given logarithmic equation is: log2 xlog2 x=4 We have to solve for x.

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: 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: The least value of the expression 2log10x – logx(0.01), for x > 1, is- (A) 10 C) –0.01 (В) 2 (D)…

A:

Q: a. find x from the equation log2 x=2 b. find x from the eqaution logx 3=2

A: Given, a. find x from the equation log2 x=2 b. find x from the eqaution logx 3=2

Q: The solution of log-(9+ x) = 2log7 8 is O x = 73 O x = -55 O x = 16 O a = 55 O x = -1

A: Logarithmic functions.

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: Which of the following is equivalent to 142 = X? O logx(14) = Z O log x(Z) = 14 O log14(Z) = X O…

A: The objective is to find the correct option.

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

A: Introduction :

Q: Does the function f(x)- logarithm of x with the base of 4 approach a certain real number as the…

A: Consider the given function as fx=log4x.

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

A: lnx y4z53 =lnx +ln y4z53 =lnx +ln y4z513  ln y4z513 =13ln y4z5 =13ln y4-ln z5 =134 ln y-5 ln z =4 ln…

Q: What is the domain of ƒ1x2= logb x2? What is the range of ƒ1x2= logb x2?

A: Given: fx=logbx2 we know that domain of logx is x greater than zero similarly, domain of given…

Q: Evaluate loge 7 by Simpson's (i) rd, and (ii) th rules.

A:

Q: = log,25 -x=

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: Find a number x such that log3 (5x + 1) = 2

A: We have to find x

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

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Q: Differentiate with respect to the independent variable: f(x)= log base 20 square root x

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Q: 2. What is the extraneous root of 2 log3(x + 4) - log3(-x) = 2?

A:

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

A:

Q: The number of positive integers satisfying x + log10 (2* + 1) x log105 + logi06 is ..

A: Introduction :

Q: Use the properties of logarithms to expand the expression y8 In x13 z16 in a form with no logarithm…

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Q: Expand loge x in powers of (x- 1) and hence evaluate log, 1-1 correct to 4 decimal places.

A: