Find w if w = x10 + 10*. dx 10* 10x° + In 10 log10 e dw dw 10x° + 10* dx dx Option 2 Option 3 In 10 10x° + 10* dw dw 10* = dx 10x° + dx log10 e

Q: Find the greatest integer less than or equal to log29 S2²10 log₂ (x³ + 1) dx + S₁ 3 (2-1) dx.

A:

Q: Show that S log(sin x) dx = -log 2.

A: To show that ∫01logsinπxdx=-log2 using the given figure.

Q: Find if z = log2 y – 6 log5 y. dy dz dz In- dy y In 10 dy y ln 10 Option 1 Option 4 64 dz In- 64 dz…

A: We know, ddxlogax = 1x·ln a a·ln b = ln ba ln a - ln b = ln ab

Q: 1-In (-) + In(2x) = In3 2- 4 log 2 - log3 + log16 = x 3-Expand In [x? sin x /Vx2 +1]

A: To find the value of x

Q: dw Find if w = x10 + 10*. dx log 10 dw dw 10 10x° + 10* 10x° dx dx log10e O Option 3 O Option 1 dw…

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

Q: A RC circuit has an emf of 310 cos 2t volts, a resistance of 170 ohms, a capacitance of 0.00167…

A:

Q: dz dz +y дх = 50 +x4°y+y5° ), Prove that x ду If z= log (x50

A:

Q: 3. Use Log Rule to integrate. a. Sor5 Sdx а. бх-5 b. S; -dx x(lnx)²

A:

Q: Express as a single logarithm. 5logbt-logb S + logb V - 4 logbu 1) logb 1/2 215 15 v1/2 ) 2) logb…

A:

Q: 2. Differentiate: a) y = log2(3x) %3D 2 b) f(x) = –7 log(x²) %3D

A:

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: 2. Find y' if y = 7* (log4 x)⁹.

A:

Q: Differentiate. y= 11* . log 7x dx (11*. log 7x) =O

A: Given that

Q: | 1-x² y = log10 2- 5x

A:

Q: Find ay dx 3. 4. 5. y = 2e³x5tanhx y = xln(5x-2) y = sec ¹(log 7x)

A: Given :y=2e3x5tanhx4. y=xln(5x-2)5.  y=sec-1log7x

Q: dy : Prove that dx or ỹ for expression y log2(x²) is equal to ỹ = 2[1-log2 x² In 2] %3| x2 x³ In 2

A: Given, y = log2x2x2    We have to prove dydx or y¯ = 21-log2x2.ln2x3ln2

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

A: This is a problem related to logarithm properties. Based on the general formula we can answer the…

Q: Find dy/dx if y=log(-4x^2+2)

A: To find the dy/dx of the given function.

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

A:

Q: [E] Prove with usual notations that (i) hD = log(1 +A) = – log(1 – V) = sinh '(u8)

A: We will prove the following result.

Q: (b) 5" (2 – cot 5")(1 – csc 5“) dx SC 11 – 2 log x (c) / dx JIV6 log r – logʻ 1 x/6 log x -

A: You have asked Only part b and c

Q: 2. If the rate of transmission of an additional case of covid-19 is 0.3 per day starting February…

A:

Q: dy Solve the initial-value problem for y as a function of r. (4 x) = 1, y(0) = 4 de…

A: Given initial value problem is,

Q: 1. y = e9z-5 2. y = 2x ln(x +2) 3. y = (2x – 5) log(3x² – 6æ)

A:

Q: If logx = 4 and logy =7, then the value of -log is %3D xy

A: Given, logx = 4  and  logy = 7 We have to find the value of  -log1xy.

Q: (b) 2log(x – 3) – log(x – 1) = 0

A:

Q: Solve for x. (a) In (x – 3) = 7 (b) In (x + 4) + In (x - 4) = 1 (c) log gx² - log ,2x = 3

A:

Q: Evaluate log2(x²) dx In(2) -log2(x²) + C 4 In(2) log2(x²) + C n(2) (log.(r2))2 (log. (x2))2 1r 4…

A:

Q: . if võ =o, i =1 and Ju = 2 estimate 13 %3D by constructing Logrange polynamial, Itn with the exact…

A:

Q: - y =log x² dy_ 8log, x A. dx dy 4log, x В. dx dy _ 4xlog, x xIn 2 dy 8x log, x D. dx xln2 xIn2 dx…

A:

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

A: Just use basics of logarithm.

Q: 2) y= log, (-4x +6)+ 4 2 +6 1) у3D 4) y= In (4x – 10) – 6 e+10 3) y =

A: SOLUTION- Since you have posted a question with multiple subpart , we will solve first three for you…

Q: calculate the integral.

A:

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: Differentiate. y = 12* • log 6x d x (12*- log ex) = D 6x) = [ %3D dx

A:

Q: Differentiate y = (9x- 11) log3 (1læ – 9). %3D A. y' = 9(11x-9)+11(9z-11) In(9r-11) (9x-11) In(3)…

A:

Q: Differentiate. y = 10 log 3X %3D d dx (10*. log 3x) =D • log

A:

Q: 2 log(x+y) = 3log3 +logx + logy

A:

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 = 3e +7 ln(2x) + log, x- 4" O y' = 15e5 ++ 1 - 4* In 4 %3D - I In 2 O y' = 15e5-1 1…

A: We have to differentiate  y = 3e5x + 7 ln(2x) + log2x - 4x.

Q: 7. Find y'. y = log, (9– x-x)

A:

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: d log, x = 1 dx [(In a)(x)]

A:

Q: 10. y = log2(sin x)

A: We have to find derivative. o differentiate given question.

Q: 1+logx 2. =D1. %3D 1. 196 16. Solve for x, 5-log:

A: We have to solve for x .

Q: 1. Find for the following functions : dx 2x (ans.: 3x' log,( 3 – 2x)-’ (3–2x )In 2 45) y=x' log,(3–…

A: