Differentiate. y= log(5x + 1) 6 (6x+1)In(5) 5 (5x+1)In(6) 6 (5x+1)In(6) o loge(5x+1)

Q: (a) log,(5x – 1) + 6 = 9 (b) 163x+1 = (4)*-1 %3D (c) In(x + 6) = In(11) – In(x – 4)

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Q: Differentiate log(x² + 1)². O (x2 + 1) ln 10 4x O 4x(x² + 1) ln 10 O 2x(x² + 1) ln 10 4(x2 + 1) In…

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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: 6. Condense the logarithmic expression 2 lnx- In(x* +1).

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Q: Find y' of y = log5(4x + 3)

A: Given that

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

A: Express in terms of logarithms of x, y, z, or w.  Given expression is log3 y5

Q: In(x-글) + In(2) = 2 In(x)

A: Please refer the attached image for complete solution. THANK YOU.

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

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Q: - Express as a single log. 3 log4 x + 2 log4. log4 y - Show your work

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Q: -3 7) log4 x = 2

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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: 4 Evaluate (logyx)'., having given, 1 1 y = log1,x + ; log,0x + log10x + . 00 1+3+5+ ..+ (2y - 1) 20…

A: We have to solve given problem:

Q: Express log (x + 1)³ – 2log (x + 1) + 3 log (x – 1)²– log (x³ – 1) as a single logarithm

A: Logarithmic equation: A logarithmic equation is an equation involving the logarithm of an expression…

Q: d Find (3"). Type In(x) for the natural logarithmic dx function.

A: we have to find the derivative of 3x

Q: (a) In (x (b) log; 2y2

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Q: 9. Condense (log4x – log4y)+2 log4(x+1) into a single logarithm with a coefficient of one.

A: Explanation of the answer is as follows

Q: log, (x – 5) + log,(x + 3) = 1 In(5x) + In x = ln(100)

A: As per guideline we have to solve the one question

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

A: solution:-

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

A: The given expression is log3xzy

Q: 5. y = - 5 log , (11x - 4) 6. y = 2 log e 4x°3 7. y = 12x² log 8x 8. y = In 25x 5x3

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Q: 2. Express as a single logarithm 4 log, x² + 3 log, ) – log, x X 5

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Q: 1. In 2x - 21n/2y³ + In(xy)² as a single logarithm.

A: since you have posted multiple question i can do first question as per pur company guidelines please…

Q: dx Evaluate log - 1+ax 1-ах

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Q: (b) 2log(x – 3) – log(x – 1) = 0

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Q: Expand the logarithmic expression In(XY^2Z^3)

A: To expand the logarithmic expressionlnxy2z3

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

A: Known fact:log mn=nlog mlog mn=log m-log nlog mn=log m+log n

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

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Q: 11. Write as a single logarithm: 1 log2 X +3 log2 Y - 3 ·log2 Z

A: To write: The expression 13log2X+3log2Y-52log2Z in single logarithm. Formula used: Logarithmic rule:…

Q: Expand the log by using the properties of log.

A: The given log function is,

Q: Write the expression as one logarithm . SNIPP

A: To rewrite expression as single logarithm. Using the properties of logarithm,

Q: 7. Use properties of logarithm to expand In (y³z²Vx – 1)

A: Property of logarithm

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

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Q: d -log(z) = dz (Z

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

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Q: Which grows faster In(x) or log (x)

A: ln(x) grows faster than log(x) Look for the graph using Desmos graphing calculator.

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

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Q: 5. y = log(7x + 3). 4²x¹+8

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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: Expand the logarithm fully using the properties of logs. Express the final answer in terms of log x,…

A: Explanation of the answer is as follows

Q: Find the greatest integer less than or equal to log29 S² log2 (x³ + 1) dx + (2x - 1)³ dx.

A: At first, we have to evaluate: I=∫12log2x3+1dx + ∫1log29(2x-1)13dx

Q: Differentiate y = - using Logarithmic differentitation. A x2x' +1

A: Given;  y=ecosx^2/[pi x sqrt(2x3+1)].

Q: d Find (2"). Type In(x) for the natural logartihtm dx function.

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Q: Expand and simplify: log4(xy^5/z^4)

A: To simplify the below logarithmic expression

Q: B. Express as a single logarithm and, if possible, simplify. 1. log, x + 4 loga y - 3 log, x 6.…

A: According to our company's guidelines I can only answer first three subparts of the question B since…

Q: 4 In2 log2 x 1-

A: At first we will change base of log2x to natural log by using base change formula. Then use…

Q: Use values of f(x) = In(x) %3D to estimate log ( 6.67 ) using 4th order

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Q: 4 If log3 (x + 1) – log3x = 2, then x equals: F - - 8. 6. G H 8. | 15

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