Simplify the following system, then find (x,y,z) the by using invers method. log,(x)' – ex + 2cos2z + lne-3 = 0 In e +- 6sin²z = -log, ÷) e2x + 2 log 109 + 3 = - /1- sin²(2z)

Q: Find a formula for the exponential function passing through the points (-1,2) and (1,8) y =

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Q: Differentiate y = log 10 (x² + 1)² A. 4x (x²+1) B. 4xlog₁0 x² +1 log e(x)(x + 1) D. 2x(x + 1) C.…

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Q: 5. Solve for x without using a calculator: log. (x) + log,(x – 16) = 2

A: The answer is found in step-2

Q: Find the Re(z) and Im(z) z=logₑ(7+i)^4

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Q: Calculate by means of the logarithm: a) x¹+2log x= 100.x log x b) log(x+2)+log(x-7) = 2.log (x-4) c)…

A: We  have to calculate this equation by means of logarithm.Note: According to the guidelines we are…

Q: Z= Logyx Find 근xx (2) 근 y

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Q: Solve  x (dy/dx) + 2y = logx

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Q: Determine the X and y nter zevos of the logari thmicc toncfion 4= logo (10x +)-4

A: Consider the given function as y=log310x+1-4

Q: (a) Given that y = 3x² () Show that log log, y = 1+2log, x (ii) Solve the equation 1+2log, x =…

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Q: (b).Solve for x: if log, x+3 log, 3=4 27**2 -6x3*3 3" x9**2 3a+3 (c). Show that %3D

A: Solution is below with full explanation.

Q: Differentiate: 3. y = log₂ (x¹ - x)

A: y = log9(x4 -x) here logerithmic function is given  dlogax/dx = 1/x(lna) use this formula and chain…

Q: d Find dr (6 log,(x) + 18)

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Q: What is the value of b so that (x) = log,(x) passes through the point (64, 3)? B -8 D {-4,4}

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Q: Find a formula for the exponential function passing through the points (-3,,) and (1,10) y =

A: Given a function passing through the points (-3,58) and (1,10) we know the general form of the…

Q: If log, 2 = x and log, 3 = y, evaluate the following in terms of x and y: 4x+2y a) log, 144= (b)…

A: Here, given that logb2=x, logb3=y

Q: g(x) = y = g-¹ (g(x)). Explain the method used. Given gx sin(log(x-2)) x²+2x-3 " determine a…

A: The method used here was to first express y in terms of g(x), then apply the inverse function g^-1…

Q: l Fied dx/dy if y Loglaha) Lag (xlogx)

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Q: x = i+i+i+ J i+vi+ vi+.. 3.

A: We only solve one problem at a time so please submit these ones by one.

Q: Evaluate the following (Express all answer in Rectangular Form): a. cotlog(1 – 4i) i b. (2e) C. z2 +…

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Q: log, = 3 log, 2– log. (x- 2z) 2 express x in terms of z.

A: Given, logzxz2=3logz2-logzx-2z We have to express x in terms of z.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.