1. Use the properties of logarithms to simplify the expressions: a) In sin 0 sin 0 In 5 b) In (4r*) – In 2 c) In sec 0 + In cos 0

Q: sun(log(1+z)) 230Log(1+ Suin2) um 2-)0 log(i+sinx)

A: We will use the result  If limx→af(x)g(x) = 00 , then limx→af(x)g(x) = limx→af'(x)g'(x)

Q: 1. Simplify. a) log, V16 b) sin- (cos) c) sin 2cos- (-)) d) e 3lns

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: Q2: Solve the Logarithms Equation. logtan nx (2 + 4 cos?nx) = 2

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Q: H-w/ prove That: の legiキ2109i @ log (i+i)=2 loy (iti) logそキ2 \ogz }2こメう

A: (1)

Q: -f (x) = e* In(5x) – et"+2 + log find f '(1) .

A: The differentiation of a function at a point gives the rate of the change of the value of the…

Q: Use the properties of the natural logarithms to simplify the following expressions sin 0 a) In sin e…

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Q: Using properties of logarithms, we can rewrite the equation as In(y) - In(x7 cos(x)), which is…

A: Consider the equation  ln(y)=ln(x7cos(x))

Q: log; e(ln 5)(arccos(x)) simplifies to O a) 5 cos(x) O b) cos(x) c) arccos(x) d) None of these O e) 5…

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Q: Express the following logarithms in terms of ln 2 and ln 3

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Q: () N f(x) = , show that f(0) and its leading differences form a geometr 5. (i) Prove that A log x…

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Q: Consider the function g defined by 1 g(x, y) = cos (Tx)+ log3 (x - y) Do as indicated. 1. Determine

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Q: a. In cot(14i) b. (3er) c. z²2z = log(-2), Calculate the value/s of z d. (1-21)7

A: Given: Let's determine the given in  Rectangular form, a) ln cot1-4i b) 3e34πii c) z2-2z=log-2,…

Q: O Find y'= for each given poblem Sinx b.) y= arc cos 15*) +3 is base of logarithm 一メナ)

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

Q: Determine the numerical value of the following expression without the use of a calculator: 100 log10…

A: We have to find the numerical value of the following expression: log101000100100+∑n=1100…

Q: 1 log(e)= In(10) %3D Use the change of base property to show

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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: . y=(cosh^-1(sec(3^x)))/log 3 Find: (y')(3^-x+1)

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: QUESTION 7 sin -' (-i) = -i log(i + /2) -i log(1 + /2) i log(1 + /2) -i log(1 – /2)

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Q: QUESTION 8 sin-1(-i) = %3D o -i log(i + /2) o i log(1 + /2) -i log(1 -/2) -i log(1 + /2)

A: Option 3 and 4

Q: Differentiate the following with respect to x (i) (a)log (cosx)

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Q: Verify the identity by transforming the lefthand side into the right-hand side.

A: Consider the given equation. logtanθ=logsinθ-logcosθ Take all the value right side of the equation.…

Q: Use definition of hyperbolic function to show that 5e2z 1 2 cosh a + 3 sinhr Hence, solve the…

A: We need to prove: 2 cosh x + 3 sinh x =125e2x-1ex and then solve: 4 cosh x + 6 sinh x =ex This can…

Q: 1. Combine log, (x – /24) + log, (x + /24) into one logarithm. 2. Solve the equation log, (x – /24)…

A: 1) From the property of the log: logca+logcb=logcab   Given; log9x-24+log9x+24 So,…

Q: 3 1 y = log| cos DIFFERENTIATE THE GIVEN:

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Q: The principal value of tan-' (2i) is :Select one 1 +i-log, 3.a 2 1 loge 3+ i .b c. None of these 1…

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Q: Find h" (x) if h(x) = log,(cos(x)) – e®z. -

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Q: a. f(x) = ln 3sqrt(2x^3+5) (Use log properties to simplify first)

A: Solve the following

Q: QUESTION 8 sin -1(-i) = o -i log(i + /2) -i log(1 – /2) o -i log(1 + /2) i log(1+ /2)

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Q: If p(x)=(x3+2x)^sinx, find p′(x).  Enter an exact answer in terms of a natural logarithm.

A: As the given function :- P(X) = ( X3 + 2X )sinx  P'(X) = ?

Q: dv (b) Find v = log( log(*/1-cosx ), Where n=666. du' 1+cosx

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Q: In arcsin x (V1-x²)arcsin x

A: Given:     ∫lnarcsinx1-x2arcsinxdx    =∫lnarcsinx1-x2arcsinxdx substitute…

Q: 6) Given that x = log, b. write down an %3D expression for b in terms of a and x. log, t that log, t…

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Q: b. y= tan(7x-3)•log 4(5 + 2x) use the Product rule (3)

A: We use product rule of derivative :d/dx(uv)=ud/dx(v)+vd/dx(u). See 2nd step.

Q: In x to show that In a loga x = Use the change of base formula loga x = x In a loga x dx dx In a In…

A: topic - derivative of logarithmic function

Q: Consider the function g defined by 1 g(x, y) = cos (Tx VT) + log3 (x – y)" Determine

A: We can solve this as follows:

Q: Verify the formulas d -[a*] = a* In(a) dx y = a* log,(y) = x. starting with let and the fact log,…

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Q: 3 y = log ( cos DIFFERENTIATE THE GIVEN:

A: The detailed solution is given below Thank you

Q: Number 2

A: To Evaluate: cos2(2-i)

Q: Evaluate the integrals. dx (Trigonometric subs.) 1) 4x² – 49

A: Given:            ∫dx4x2−49

Q: log 10 6 – 1 then the value of 32 If log 10 sin x + 4 2 log 10(sin x) + log (cos x) is

A: Introduction :Given , then we have asked to find the value of

Q: b) Given that log, (y-1)+log,|| |= z and log, (y+1)+log, x = z-1, Show that y? =1+8² and find the…

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Q: -i Log TT 0.69 i TT -0.69 – 2i TT -0.69 – i TT -0.69+ i- || 2.

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Q: Evaluate the base (3-4i) logarithm of 10e^2.05i. Express your answer in a rectangular form in 4…

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Q: The integral of the square root of the difference when the square of t is subtracted from 2, with…

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Q: Determine the general solution of (cos x cos y - cot x) dx (sin a sin y) dy, Show your solutions and…

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Q: T + log, (V27 - 2") sin 24-1 + log, (log; (915) + п1+(-1)17 + 1) + (-1)5 + (-1)27 (-1)766 25 – 24 –…

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Q: . Consider the function g defined by 1 g(x, y) = cos (Tx y) + log3 (x - y) Do as indicated. 1.…

A: As per policy, we are allowed to answer only 1 questions at a time. So, I am answering the first…

Q: Use these formulas to express the numbers in terms of natural logarithms. 61. sinh-' (-5/12) 63.…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Determine the equivalent of log4i sin(3 – 4i). Express your answer in rectangular form.

A: The given problem is to evaluate and simplify the given complex expression and express in the form…