Ex. 17 The value (1+ x) of ] x (1+ xe*)? dx, is equal хе 1 + C (1+ xe*) (a) log + 1+ xe* xe* 1 (b) log + +C 1+ xe* 1+ xe* xe* 1 + C 1+ xe* (c) log 1+ e* (d) None of the above

Q: Let f(x) = log₂ (x²+2x+1) and g(z) = log₂(x+1), find h(x) = f(x) + g(x). Oa) h(z) = 0 Ob) h(t) = 2 O…

A: This question can be solved using the concept of logarithmic function.

Q: |Example 6.12. Prove with the usual notations, that (i) hD = log (1 + A) = - log (1- V) = siiih- (E)…

A: Please find step by step solution below:

Q: Which of the following is an equivalent equation to 10* = 430? %3D A) log 430 = x C) log, 10 = 430…

A: Logarithm is inverse of exponentiations. A logarithm is easy method to express large number and to…

Q: 19. If log (*+²) = (log x + logy), prove 4 2 2 that x + y = 18xy

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Q: ab, 8) Simplify log2(-) 3

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Q: 1. a. Express using index notation 5 = log10100000 b. Express in the form logab = c 26 = 64

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Q: 3x (37) 2y (d) In (e) log₂ (x³) (f) In (2x³e4)

A: Expanding given terms.

Q: Convert the following into an equivalent expression: (log -> exponential) a) p+2 = 4log₂ (2q³-1)+1…

A: The given expression,(a) (b) The aim is to find the equivalent expressions.Note: Since you have…

Q: 4. Solve for x. a) log₂ x=9 52 b) log x=- c) log, 9 = -2

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Q: 1. Show that (a) Log(-ei) = 1 - ži;

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Q: 26. What is b if (log₁x) b = 1 -? 3x

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Q: Find fx) if fx) = logX-5 %3D x4-3

A: f'(x)=?

Q: Evaluateſ dx xlogxlog(logx)log [log(logx)]

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Q: The domain of the logarithmic functiort f(x)=log_(a)x is

A: We find domain of the logarithmic function f(x)= logax.   Where, a > 0 is a constant.

Q: If log A = B = с || 18,9 x (2014) = = Alog(x) + Blog(y) + Clog(z) then

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Q: Differentiate with respect to x:* y = log, (x) :() 2+ In x - In x Option 2 Option 3 2 - In x 1+ In x…

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

Q: 4. Solve for x log (35-x³) log (5-x) = 3

A: Given: log35-x3log5-x=3To find: Value of x.

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: Show that log,(n) € O(log,(n)) for any b>0 with b 1· Generalize this result.

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Q: 10. Prove that (log2 3)-1+ (log4 3)-1 < 2.

A: Simplify the powers of the term (log23)-1+(log43)-1 by writing the terms as fractions.…

Q: 5. Determine if the following are true or false. loga logb _a) log = logx – 3 logy d) log %3D 3 _b)…

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Q: Let b be a real number. By considering properties of exponential functions, show that the points…

A: We know, for any real number b &gt; 1,         b0 = 1      =&gt; logb(b0) = logb(1)       =&gt;…

Q: 4. Show that id 5D accuracy is required to calculate the value of log(1+x) at x=0.1,0.5 by using the…

A: Given equation is log1+x=x-12x2+13x3+.....+-1n+1nxn+Rn+! So, Rn+1=-1n+2n+1xn+1 So, maximum relative…

Q: 3. Express as a single logarithm: 3 log 2 + log x - log (4x) log(8x) A. log(4x) В. log (2) C. log…

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

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Q: Determine if the root is a rational or irrational number. Explain your reasoning. (a) Part A V10 B…

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Q: In 2 log2x

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

Q: 7. Differentiate y = log10 (x² + 1)² b. 4xlog10e x²+1 a. 4x(x² + 1) c. log e(x) (x² + 1) d. 2x(x² +…

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Q: IV. odvice veren V. Directions: Use the laws of logarithms to expand the expressions as the sum,…

A: " Since you have posted a question with multiple subparts, we will solve first three subparts for…

Q: Show that || (A(st) + A(s)A(t)) dsdt = 2.x log x + 0(x) as x → 0o. JU(4)| log°x s 2 // |u() dsdı +…

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Q: 15. Solve each equation for x. b) 9*-1 = 31+ c) In(x+4)+ln(x-2) = 0 l+x a) e2" = e¤²–3 d) log +log 3…

A: (a)

Q: 16. Solve. a) log (²x) = Text 2 b) log4(x²7x − 18) - log4(x + 2) = 3

A: a) log3⁡(2xx−7)=2