Q3a & b 2) Given that log, 5 = n find the value of 27".3) Solve the following equationsa) (s')(5-)= 10 (b) In (x²-15) = 0c) log, x = 9 log,3d) 9*-3**2 -36 = 0; leave your result in terms ofnatural logarithms4) Find the real values of x for which32r01 – 12(3*)+9=05) Given that a* = b = (ab)" and that%3Da>1, b>1, xy #0 show that x+y = 1.6) Given that x = log, b, write down an%3Dexpression for b in terms of a and x.log, tlog, sHence prove that log, t=7) Solve the equation log, x-4log, 3+3=08) Find the positive value of x which satisfies theequation log, x= log, (x+6)%3D9) Solve for x and y in the following pair ofsimultaneous equations log (x+y)% 3 %3B2 log x = log (y+1)%3D

Answered: Image /qna-images/answer/90e5d392-4e0e-4eb7-8cb9-7afb05fc0981.jpg

Answered: 3) Solve the following equations a)…

Math

Advanced Math

3) Solve the following equations a) (s')(5*1)=10 (b) in (x²-15)= 0 %3D ||

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 16EQ

See similar textbooks

Related questions

Q: By the alimination of the arbitary constants a and b ,obtain the differential equation of which…

Q: 4. Use Euler's method with a step size of h = 0.2 to approximate the solution to initial value…

Q: 1. Solve the linear differential equation of y' – 2xy = = X. swer:

Q: .3) Find the solution of the folowing differential equation: in{z) +]

Q: A tank contains 50-liters of brine in which 20 grams of salt is dissolved. Pure water is being…

A: Given: Let the rate of pumping in, Rin = 5 L / min Let the rate of pumping out, Rout = 4 L / min

Q: 4. Apply to the initial value problem y' = -ry + 1, y(0) = 0 three steps of the Picard-Lindelöf…

Q: I am still having troubles trying to effectively solve e^6x(cos7x)dx by integration by parts.

A: Let u = cos7x , dv=e^6xIntegrating by parts:

Q: 3. What is the difference between a solution of a differentialequation and a solution of an…

A: The solution represents a family of solutions all of which satisfy the system of differential…

Q: Solve the separable dr +rtanodo= 0, r(x)=2. equation (initial value problem)

A: givendr+rtanφdφ=0dr=-rtanφdφseparate variables1rdr=-tanφdφintegrating on both side

Q: 2. Solve the first-order linear differential equatio a. y' + 3y = e3x

Q: Q4// Solve the partial differential equation a²u ди cos*x given that = x when y=0 and u=3 when x=0?…

A: The given partial differential equation is ∂2u∂x∂y=cos4x Integrating on both sides with respect to y…

Q: 4. Which of the following represents the differential equation of the family of parabola having…

A: Follow the procedure given below.

Q: For the Initial Value Problem given below:

A: Given, dydx+2y=2-e-4t, y(0)=1

Q: 4.Determine if the given function is a solution of the given differential equation

Q: x²(a+x) 2. Family of strophoids with the equation y² %3D a-x

Q: State the order of the given ordinary differential equation. (sin 8)y"" - (cos 8)y' = 2 Determine…

A: Part 1: Given the ordinary differential equation, (sin…

Q: Show that y - In(x +1) is the solution of the differential equation of (1+ x*)y= 4x':

A: Use the formula below to perform the differentiation .

Q: 3: The dimensions of a rectangular box are measured to be 75 cm, 60 cm, and 40 cm, and each…

Q: Find the general solution to the differential equation 3y" + ry' + 3y = 0 If your answer involves an…

Q: f (x) = y = x³ +x– 10 = 0

A: Using Newton raphson method.

Q: Solve the initial value problem. 4 y(x) = 4 sec(3.x) tan(3.x) ; y(7) = %3D 3

A: y'(x) =4 sec(3x) tan(3x)y(x)=∫ 4 sec(3x) tan(3x) dx3x=t,dx=dt3y(x)=43∫ sec(t) tan(t) dt =43 sect…

Q: Find the particular solution that satisfies the differential equation F'(X) = 10x − 12x3 with an…

A: Given the differential equation: F'x=10x-12x3 Initial condition: f3=2

Q: 11.Solve dy - x+) y(2) = 2 by Fourth order Runge-Kutta Method at x = 2.5, and x = 3 %3D dx

Q: Use variation of parameters to solve the given initial-value problem. x'=(³₁3¹)x+ (4²).X (0) = (¹)…

Q: Obtain a differential equation associated with the primitive Ax^2+By^3=9

A: Differential equation is obtained by eliminating the constants A and B from the primitive equation.…

Q: 5. Find the solution of the differential equation using Variation of Parameters. у" - Зу" + Зу 3 E

A: Given y'''-3y''+3y'=exx

Q: 21. Find particular solution of the differential oquation-2(x+ 1) Y.given x 0,

A: Givne that The differential equation To find the particular solution of the differential equation

Q: Find the general solution of the differantial equation www y' = xy around xo O by power series.

A: We will find out the required general solution for given differential equation.

Q: Write in your words about some of the applications of the partial differential equations With…

A: Given :- some of the applications of the partial differential equations

Q: 6. Show that 2y2 dy x² + y2 dx is homogenous equations. Hence, solve the equation.

Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

A: Here we need to solve the given differential equation.

Q: 3. Show that the differential equation zxy

Q: 5) Use the variational iteration method to solve the following Volterra integral equation by…

Q: Solve the initial- value problem:

A: We are given the Problem: ⇒dydx=cos x-sin x+y ⇒dy=(cos x-sin x+y)dx Now , integrating both sides, we…

Q: 3. Obtain the differential equation of the family of straight lines passing through (0.1). SAdd File

Q: Find the particular solution that satisfies the differential equation and the initial condition.…

A: To find The particular solution that satisfies the differential equation and the initial condition.

Q: Show that: a) The price of the stock itself, that is when u(t, X1) = X1, solves the…

Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

Q: 4. Find a particular solution of y" + y' = cost cos 2t cos 3t.

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

Q: *-({ 3*+(tans

Q: Solve the given differential equation by using an appropriate substitution. The DE is of the form -…

Q: =5. (b) Solve the following initial value problem f'(x)= 6cos2x – 3 sec² x, f

Q: which 20 grams of salt is dissolved. Pure water is being pumped into the tank at a rate of 5…

Q: 4. x" +x=e+!.

Q: Find the differential equation whose solution is given by y^2=4ax

A: topic - differential equations

Q: 3. Solve the Euler-Cauchy differential equation d²y dy 3x +4y= ln² x – In x dx² dx

A: Given an Euler-Cauchy differential equation, x2y"-3xy'+4y=ln2x-lnx Re-writing it in the standard…

Q: Find the solution of the initial value problem substitution y-erX in to given defind

Q: Solve the given differential equation by finding, as in Example 4 of Section 2.4, an appropriate…

Question

Q3a & b

2) Given that log, 5 = n find the value of 27".
3) Solve the following equations
a) (s')(5-)= 10 (b) In (x²-15) = 0
c) log, x = 9 log,3
d) 9*-3**2 -36 = 0; leave your result in terms of
natural logarithms
4) Find the real values of x for which
32r01 – 12(3*)+9=0
5) Given that a* = b = (ab)" and that
%3D
a>1, b>1, xy #0 show that x+y = 1.
6) Given that x = log, b, write down an
%3D
expression for b in terms of a and x.
log, t
log, s
Hence prove that log, t=
7) Solve the equation log, x-4log, 3+3=0
8) Find the positive value of x which satisfies the
equation log, x= log, (x+6)
%3D
9) Solve for x and y in the following pair of
simultaneous equations log (x+y)% 3 %3B
2 log x = log (y+1)
%3D

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Orthogonal Vectors$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.