Logarithms Definition and 257 Threads

Hi there Can someone please review my work and advise. Homework Statement Given log(a)b=3 , use the properties of logs to evaluate 4log(a)(1/b)+2log(a)b^3 Homework Equations I used the rules log(a)1 = 0 log(a)(x/y) = log(a)x-log(a)y log(a)x^m = mlog(a)x The...

An Earthquake measures 6.1 on the Richter Scale. What is the rating on an earthquake that is twice as powerful? I = I0 × 10M I-intensity of earthquake I0-earthquake with intensity of 0 M-magnitude of earthquake on the Richter Scale So I figured I'd use I1 = I0 × 106.1 to find the...

Homework Statement Homework Equations The Attempt at a Solution I have no idea how they came up with 7/2 as a solution...can anyone tell me how? I am not sure how logarithms and square roots work...how did they get the 1/2 exponent over the second 2? What is the...

If log103 =0.477 then the number of digits in 340 will be? 100.477 = 3 10(0.477[SUP]40)=3[SUP]40 hm...?

Homework Statement I tutor math for a couple of high school kids, and usually don't have any problems. Occasionally we run into a problem that takes me a minute, since I haven't actually used a lot of this stuff since I was in high school, but I always figure it out very quickly when that...

Homework Statement log2√xHomework Equations The Attempt at a Solution I thought that it might be something like log2x - log2x but that's not right. The book examples don't have any radicals.

My textbook says O(3log2 n) can be written as O(nlog2 3). Why is that? Thank you.

Homework Statement Log(exp(10i)) The Attempt at a Solution Since we want to get this in terms of the principal argument, would it matter if we ultimately wrote i(10 - 3\pi) or i(10 - 4\pi), since they are both in range?

I don't know why but when I'm solving a huge problem and I end up having to use logarithms I find it frustrating since they take most of my time up since I haven't studied them very often, and they're not very interesting in my opinion. What's your opinion on logarithms? Do they appeal to...

1. Determine the equation y=f(x) for each of the following cases in simplest form. All of the plots are straight lines and all coordinates are indicated with abscissa first, ordinate second (x,y). -log y versus log x on a rectilinear graph passes through (5,7) and (2,3) -(y-2)^2 versus x...

First of all I would like to share this because I randomly found it and I commonly see that people approach base changes of common logs on the ti89 titanium in a very different way. Scroll half way down page 2...

Homework Statement What is the derivative of y=x^(13/x^2) with respect to x? The Attempt at a Solution I went through multiple techniques to solve this, but all of them have failed so far ._. In my latest attempt, I took the natural log of both sides: lny= lnx^(13/x^2) I...

Homework Statement Solve the compound interest formula for r by using natural logarithms. Homework Equations A=P(1+r/n)nt The Attempt at a Solution 1400 = 1000(1+r/360)(360*2) 1.4 = (1+r/360)720 ln(1.4) = 720ln((360+r)/360) I'm not sure where to go after this. Did I...

Homework Statement We're working with logarithms of base 3, and log(4)=a and log(7)=b. The goal is to put log(21) in terms of a and b. For example, take the log(112). It's the same thing as 2a+b since 4*4*7 = 112. Homework Equations Just the standard log properties. The Attempt...

I'm a novice at MATLAB so I apologize if this is a dumb question: I need to find the sum of A, B and C given X, Y and Z, where ln(A)=X, ln(B)=Y etc. However, the values A, B and C are so small that when I try to use 'exp' the result is rounded to zero. This is a problem because later in my code...

I've become rather curious, as of late, about the realm of complex logarthims; more specifially logarithms in the form log(z) where z is any negative number. Excuse any ignorance on my part, as I'm only in Precalculus, but I was just curious to see how Euler's formula is related to complex...

I recently had a test (precalc) where we had to solve log(x)-log(x+4)=2 for x. The answer comes out negative. I understand that in precalc we are defining the logarithms for just positive numbers, but- Is it ever justified to define a logarithm for all numbers, both negative and...

Homework Statement Express in terms of logarithms x, y, z or w. Problem: loga(x8w/y2z4) Homework Equations log(u/w) = log u - log w log(uw) = log u + log w The Attempt at a Solution Here are my attempts: As you can see, the answers are pretty similar. I'm assuming...

Homework Statement Solve the simultanious equations 2log_2y = log_43 + log_2x 3^y = 9^x The Attempt at a Solution 3^y = (3^2)^x y = 2x 2log_2 x + 2log_2 2 = log_2 \sqrt{3} + log_2 x log_2 x = log_2 \frac{\sqrt{3}}{4} No idea what to do from where, what does x equals?

Homework Statement I'm going to post an image due to the complex syntax in the problem... The Attempt at a Solution I'm not going to lie... I really have no idea where to even begin with this problem. Because it says total distance traveled by the particle, I'm assuming that the...

Homework Statement A security PIN code is four digits long. Each digit could have the value 0 to 9. if an office building needs 10 security PINs, express the number of codes in logarithmic form with base 10 The Attempt at a Solution y=4log(x-10) I don't know how to do the...

Homework Statement Find the exact value of x if: Homework Equations (3x)lg3=(4x)lg4. The Attempt at a Solution 3lg3xlg3=4lg4xlg4 (xlg3)/(xlg4)=(4lg4)/(3lg3) xlg3-lg4=(4lg4)(3-(lg3)) xlg(3/4)=(4lg4)(3lg(1/3)) Please help me, I am stuck here!

Homework Statement Solve for x xln(x)-24+6ln(x)-4x=0 My attempt at the solution I first moved "-24" and "-4x" to the right side of the equation yielding xln(x)+6ln(x)=24+4x I then converted the natural logarithms to exponent form and product form yielding ln(x)^x+ln(x)^6...

Homework Statement NEED HELP WITH THIS MATH PROBLEM: LOG3(X+3) + LOG3(X-1) = 1Homework Equations The Attempt at a Solution I SAID LOG3(X+3) + LOG3 (X-1) SIMPLIFIES TO LOG3(X+3)*(X-1) = 1 I.E LOG3(X^2 +2X - 3) = 1 THEN 3^1 = (X^2 +2X - 3) AND 0 = (X^2 +2X - 6) THEN USE THE QUADRATIC FORMULA TO...

Homework Statement NEED EXPLANATION HOW TO SOLVE QUESTIONS 46 AND 47 http://img685.imageshack.us/img685/2259/101020114327.jpg Uploaded with ImageShack.us Homework Equations The Attempt at a Solution

What's the point of logarithms when trying to sketch functions? Isn't y=3^x the same as x=3^y? I think it should be the same, but I get different results for each method. If it is the same, what's the point of y=log3x? It's confusing and I don't get the same results when trying to find the...

I'm unsure as to if I am using the correct terminology, but what I mean by this is log = logarithm in base 10. ln = logarithm in base e. logx = logarithm in base x. Upon some investigation, I found that log(a)/ln(a)=log(b)/ln(b) where a and b are constants, meaning that there is a ratio...

When Logarithm are Defined as integral and the Exponetial functions are defined to be its inverses , then What can prove ? or why ? a^n = \underbrace{a.a.a...a}_{n-times} : n\in N also Why we define rational exponents as roots? I am sorry If my Question is silly. IS my Question...

Homework Statement Sec(x)/((ln(tan(x)+sec(x))^1/2) We were instructed to find the integral Homework Equations Here is a link to the wolfram solution, i don't understand the steps they...

This question is not about how to calculate the logarithm, but rather what method would be expected of someone in 1969. I am going through Apostol's Calculus, and in section 6.10 Apostol introduces polynomial approximations to the natural logarithm. Specifically, he introduces the following...

The Problem is when I Compute the Inverse I have to solutions sech^{-1}(x) = ln(\frac{1\pm \sqrt{1-x^{2}}}{x}) : 0<x\leq 1 And this not function which of them I will choose Another Question is how can I prove without the graph that csch (x) is one - to -one thanks

Homework Statement Show that ln[ (N + M - 1)! /M! (N-1)! ] is equal to N ln((N+M) / N) + M ln((N+M) /M). Homework Equations Using stirling's formula ln N! ~ N lnN - N The Attempt at a Solution ln[ (N + M - 1)! /M! (N-1)! ] (a) = (N+M...

How were logarithms calculated before the use of calculators.

I was just curious. I believe the answer would be no, but I don;t know why

Hey guys I need help how to solve this equation... Express your answer to the equation in the form alnb 9e^4x-e^2x=0 This is as far as I got 9e^4x=e^2x ln(9e^4x)=ln(e^2x) the answer given in the markscheme is x=1/2ln1/9, x=-1/2ln9, x=ln1/3, a=-1/2 and b=9, x=-ln3 (accept a=-1 and...

Homework Statement Perhaps this is trivial, but working in thermodynamics oftenly requires of handling with logarithms. For example, in an exercise I'm trying to solve, I need the roots for something like: x+ln (x)=constant The thing is I don't know how to find this kind of roots. I mean, I...

Homework Statement Ok I'm taking an online advanced function course, and we are on logarithms and I don't get it one bit , there two questions given to me 1. y = 2 log10x and y = log5 (x – 2), Homework Equations The told me to make a table of value , i don't understand how i will get the...

Homework Statement Solve the compound interest formula for t by using natural logarithms. Homework Equations A=P(1+\frac{r}{n})^{nt} The Attempt at a Solution I start by dividing both sides by P. I then take the natural log of both sides and end up with ln(\frac{A}{P})=nt *...

Homework Statement Use Natural Logarithms to solve for x in terms of y y = \frac{e^{10x}+e^{-10x}}{e^{10x}-e^{-10x}} Homework Equations I am not too sure. The Attempt at a Solution I multiplied both sides by the denominator first. Then I multiply by an LCD of e^{10x} I end up...

Good morning everyone. Can someone please explain to me how you get results for logarithms. I understand that 10 power of 3 = 1000 but how do I work it out as Log10,1000. I know this is a strange request, but I can't get my head around it. Thank you

How can I force : A Log[b] + A Log[c] to simplify to A Log[b c]? I tried, A,b,c all elements of reals, but it doesn't do it. (Assume everything is Real) I know I can make some patterned rules but I'd rather have it be by default. (i.e. : a_ Log[b_] + a_ Log[c_] :> a Log[b c])

Hi, If I have ln{a} converging to ln{b}, can I claim that a converges to b? I would think yes, because ln is a monotonic function and we are always sure to get a unique value of ln for any argument 'a'. Is that reasoning correct? I am not able to prove it by the definition of...

325*(0.8)^t=5 Can anyone help me please?

Homework Statement Find the equations of the tangents to the following graphs for the given values of x. (a) y = ln x, where x = 1/2 Homework Equations The Attempt at a Solution I know ln x differentiated is 1/x but I cannot see when the rest fall into the place. The book I'm...

Homework Statement When was trying to solve this problem cos(x)=-2 I got the following answers i ln(2 +/- sqrt(3)) + 2 pi n n set of integers positive and negative now I was told by a couple of people on here to add 2 pi n to my solution because before it didn't have it. At the time I...

Homework Statement Let v = 1 / kt v = m/s k = 1/m t = s v = dx/dt so dx = dt / kt integrating, x = ln (kt)/k + C However the argument of a logarithm is dimensionless. But an integration is a perfectly normal thing to do. So how come this integration results in a...

!Logarithms and Index Laws help! Ive been trying to complete a revision sheet but it has logarithims and index laws, and i don't know how to do them. I've included a few of the hardest questions frome the revision sheet in the attachment. ...Look at attachment.... I've tried the...

Ok, I have an Expression which is attached and it needs simplifying. What I have done is got 12logx But I don't think this is correct. Another possible place I got to is logx4/logx1/3 Which one is it?

Simplify the attached expression using any relevant logarithmic rules I haven't really done much with logarithms, so i didnt know where to start?

Homework Statement ∫tan^2(2x)/sec2x dx; u=sec2x; du=1/2tan^2(2x)dx. Homework Equations ∫1/x(dx)-ln|x|+C. ∫1/u(du)=ln|u|+C The Attempt at a Solution This is me trying to rewrite the equation. (sin^2(2x)/cos^2(2x))/(1/cos2x), (sin^2(2x))/(cos(2x)). Honestly, I feel lost trying to...