d -log(z) = dz z O O 2- 1

Q: (log a)* d.x 1+x²

A: Given ∫0∞logx41+x2dx we can write the above as…

Q: dy (x² + 1)? if y = 2) Find dx (x² – 1)³ a) without the aid of logarithmic properties b) using…

A: Here we have to find the the derivative of y

Q: Find the first six terms of the expansion of the function e^x log(1+ y)

A: We have to find the first six terms of the expansion of the function              exlog1 + y Here ,…

Q: e In 11 – log 33 ™ + log 100

A:

Q: 8. In V5x 3 y z2 9. log. V xt 10. loga Va b5

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Q: Find dx by first using algebraic properties of the natural logarithm (x+7)(x + 8)³ (x + 2)°(x + 3)°…

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Q: e-2x 2+x In 3x csc' x -) f(x)=. b)Use logarithm to differentiate: y = (3х-1)

A: a)f(x)=ln(3x)csc2x-x5e-x3f(x)=sin2x. ln(3x)-x5e-x3differentiating w.r.t…

Q: Log(X^3Y^2Z^7)

A:

Q: dy et y = (x³ – 18x)m(=). Find using the method of logarithmic dx - ifferentiation. Express your…

A: Topic:- derivatives

Q: +y log z =0 is 1S

A:

Q: (a) Find if y(x) = log3(729) sec(In(r)) + In()r+ e

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Q: (iv) log, r – log,(r – 1) = ; (v) 41-z = 32r+5 () -- (vi) 2x In = 0

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Q: 25łn²(x) log (x) dx

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Q: x° -1 The value of the integral dx, (a > 0) is log x

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Q: Find the solution for x: log (Vz+1+1) log V- 40 -3

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Q: Differentiate the function

A: Before we get into solving the question, let's look at the two derivtives shown on the white…

Q: Differentiate g (†) = 4 log, ( t ) – In ( t )

A: Given g(t)= 4log3(t)-ln(t) Now we have to differentiate g(t) as shown below

Q: z² – 2z = log(-2), Calculate the value/s of z

A:

Q: y = log, x is equivalent to the exponential form %3D x > 0, b > 0, b # 1.

A: To fill in the blanks

Q: d (log4 Vsin x) dx

A: We have to find dlog4sinxdx.

Q: (C) y = -log3 x (G) y = log3(1 – x) (A) y = log3 x (B) y = log3(-x) (F) y = log3(x – 1) (D) y =…

A: Find the following graph:A) y=log3xB) y=log3(-x)C) y=-log3xD) y=-log3(-x)E) y=log3x-1F)…

Q: 1. Find the value of y. a. log;25 y b. logy32 = 5 c. log,y

A:

Q: b log (x) – d log(v) + log (z)

A: Given,           b logcx - d logcy + logcz

Q: Find d/dx(2^x) Type ln(x) for the natural logarithmic function.

A:

Q: 11 2 log a dx aV6 log r- loga

A:

Q: Find the value(s) of x for which the equation is true. log(x + 3) = log x + log 3

A: We have to find the value of x for the given equation: logx+3=logx+log3 We know the properties of…

Q: Combine into a single logarithm. In(x – y) – 2 In(x² + y²) OIn (x-y)3 In (x²+y²)* In Va-y) (x²–y²)?…

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Q: log log (y) = A * e ^ x + B * e ^ (- x)

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Q: e: Sz dx (x+1) log(x+1)

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Q: . z² + 3z = log(-3), Calculate the value/s of z

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Q: 5. ƒ(x) = 10* . ex 2x-x2 a. 2 b. logze e 10 c. e*10* + loge e*(x-3) d. x²-4x+4 e. 4x²(3 log, x +…

A:

Q: y = log, x %3D 1 1 1 2 4 8. 16 8 4 2 y.

A: given y=log2x complete the table x 116 18 14 12 1 2 4 8 y

Q: If T = 1o, then log T is equivalent to: 5 A (1 +2 log x) – log y B log(1 +2x) – log y (1- 2 log x) +…

A: We can find the log as below

Q: (а) е" =D1 %3D (b) log(x – 3) + log(x - 6) =

A: Given that: (a)ex2-9=1(b)log(x-3)+log(x-6)=1

Q: d.) In (z+9)– In z = 1 2 log Vx? + 21x = 3 e.) In(x+1) c.) In (x –1) = 2

A: (d) To Find: The value of x. Given: The equation is ln x+9-ln x=1. Formula used: ln a-ln b=ln ab If…

Q: 4 log x + 20 log y- 12 log z

A: We will use basic log properties to solve this

Q: 1/2 (log.(e))" (b) dt. 2t

A:

Q: Find the integral: log2 X dx In(2)/ 082(x) + C 2

A: Put logx = u then solve it.

Q: d (d) (log3(x) – tan¬1(x)) dx

A:

Q: Find d (7ª). Type In(x) for the natural logartihtm function. dx

A: Given query is to find derivative if the expression.

Q: d 1 -(log, (x))= dx x > 0 x In a

A:

Q: dx Express your answer in logarithmic form. x2 + ax

A: ∫dxx2+ax

Q: e) log(x + 5) + log(x) = log(6)

A:

Q: f (x) = ex ln(5x) - ex^3 +2 + log(e2x^2), find f '(3)

A: The given expression is f(x)=exln(5x)-ex3+2+log(e2x2).

Q: (a) f(t) = In(5t - 4) 12 (b) g(x) = log(x² - 25)

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Q: b) Find the value of x that satisfies log(x+3)− log x = log x+log 2.

A: Follow the procedure given below.

Q: dx Evaluate: s (x+1) log(x+1) A --In 10 log² (x+1)+C 2 B In10 In[log(x+1)] + C с = -log² (x + 1) + C…

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Q: Find dy dx given (х* + 3x — 1)° /1 – 3x³ y , by using property of logarithms.

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Q: 2 log3 (x) + + log3 (y) is equivalent to: 2 log3 (ry) O log3 (2ry) O log, (2*y) O log, (zy)

A: