(i) Given that log, x+2 log, y = 4 show that ry 16. Hence solve for x and y the simultaneous equations: log, x+2 log, y = 4 log(x+y)=1 (ii).Find the values of y which the equation: (8')'-32 1 4.

Q: Solve x*+6r34y dx+ +3x=+y = (1 + logx)* dx²

A: Given differential equation, x4d4ydx4+6x3d3ydx3+9x2d2ydx2+3xdydx+y=1+logx2 This is a homogeneous…

Q: x = log, 5 y= log, 2 log, 60. in terms of x and y. A) Given that and rewrite C) Solve for x:…

A:

Q: a log(bz + cиw)

A:

Q: Write the expression x- y log7 49z in terms of A = log, x B = log, y %3D and C = log, z

A:

Q: Solve: log, -z + log, (9z – 6) = 0 8 4 2 3' 3 I = 1 No solutions ||

A: Given: log9-x+log99x-6=0

Q: 4. If p = a + b + c a. Determine the range of g(x) = e b. If aa = bb = c . -12x-11 ab log.(ab) _ bc…

A:

Q: 3. The solution set of = 4 is log, Vr+ 2 21 B (-3) C (2) D (-3 2)

A:

Q: Solve the following logs and write the final answer to the simplest form. 1) log8 a2 2) log15 *'y8…

A:

Q: = sec(0) – 6 = 0 sec(8) = sec(0) + 1 = 0 sec(0)

A: Topic-trigonometry

Q: Simplify and solve log; v9.

A: We have to simplify and solve the expression log59

Q: i) log, (5x + 4) – log,(4x) = 2. ii) 9e* + 4e-x – 12 = 0.

A:

Q: f(z) = a log,(Vdecz

A: Given, z = 8 + 9i  when  a=50 , b = 7, c = 10,  d = 12 and n = 6 .

Q: 1) Solve for x and y in the following simultaneous equations *a) log, x = 2; 5y= x +12 log, y *b)…

A: We have to solve for x and y in the following simultaneous equations.

Q: Solve for x sin(log2 (13x² +16x34) = y

A:

Q: Use cofunctions of complementary angles to find θ where cos(17deg) = sin(θ). Use logarithm…

A:

Q: 6. Solve the logarithmic equations below: log3 (p – 2) + 9 = 12 b. - 3log4 (2p + 3) – 1 =- 4 а.

A:

Q: 2) If x=0 and y=5 Check if the following statement is true. Explain and show your work. log, (5x –…

A: log of negative number does not exist

Q: Let q= eJZ and cloga (bx)Loga (ě) 子()= where b=3 and c=-s C= - S Caleulate 3e7'ce) oוא

A:

Q: j. 1 dx = TT log,2 Vex - 1 Solve the equation

A:

Q: L = Tan (log2xyz) solve = ∂4L/∂x2yz

A: Given, L=tanlog2xyz Find the value of ∂4L∂x2∂y∂z.

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

A:

Q: log (x+8) ) dx 3

A:

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

A:

Q: 4. Solve the equation log, (x - 3) + log, (3x – 2) = log, 18. Round answers to two decimal places. V

A:

Q: Ive the following equations (a-c). Give an exact and an approximate answer to two decimal places:…

A: We have to find

Q: Can you please do number 13 and show the steps of x and y intercepts

A: To determine the intercept on x-axis, y-axis and draw the graph of given function.

Q: i) Rearrange this equation to make S2 the subject AG = AH – T (S2 – S1) ii) Rearrange this equation…

A:

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.