Logarithms Definition and 257 Threads

I can most of the time successfully convert between base 10 and another base or another base and base 10 or between 2 bases where one of them is a power of the other(like base 2 and base 4 or base 3 and base 9). With negative bases I sometimes don't get what I want in that negative base and...

the variables x and y are positive and related by x^a.y^b=(x+y)^(a+b) where a and b are positive constants. By taking logarithms of both sides, show that dy/dx=y/x. provided that bx not equal to ay.

Homework Statement Solve for the point of intersection between ##y=\log_{2}{(2x)}## and ##y=\log_{4}{(x)}## Homework Equations 3. The Attempt at a Solution [/B] Setting the two equations equal: $$\log_{2}{(2x)}=\log_{4}{(x)}\\ 2x=2^{\log_{4}{(x)}} \\ 2^{2x}=4^{\log_{4}{(x)}}\\...

1. The population of a certain country grows according to the formula: N = N0e^kt Where N is the number of people (in millions) after t years, N0 is the initial number of people (in millions) and k = 1/20 ln 5/4. Calculate the doubling time of this population. Leave your answer in terms of ln...

Working on a personal music project, I would like to pull 'z' out of the logarithm below if I can help it, but am having trouble: It's a portion taken from this: Which evolved from... However, this is only the mathematical modeling of the object. The actual *physics* aspect...

I was crunching through some logarithm questions for homework when I noticed this. I was wondering if any of you have any incite on what causes these two numbers to be exactly 1 unit apart from each other. I found it very odd, and I am wondering if there is some kind of relation here that I am...

Find the minimum of $\large \log_{a_1}\left(a_2-\dfrac{1}{4}\right)+\log_{a_2}\left(a_3-\dfrac{1}{4}\right)+\cdots+\log_{a_n}\left(a_1-\dfrac{1}{4}\right)$ where $a_1,\,a_2,\cdots,a_n$ are real numbers in the interval $\left(\dfrac{1}{4},\,1\right)$.

Homework Statement On very hot days there sometimes can be a mirage seen hovering as you drive. Very close to the ground there is a temperature gradient which makes the refraction index rises with the height. Can we explain the mirage with it? Which unit do you need to extremalise? Writer the...

Homework Statement Find the largest set D on which f(z) is analytic and find its derivative. (If a branch is not specified, use the principal branch.) f(z) = Log(iz+1) / (z^2+2z+5) Homework EquationsThe Attempt at a Solution Not sure how to even attempt this solutions but I wrote down that...

I've a small confusion about formula ##\log^3 n = \log \log \log n## or ##\log^3 n = (\log n)^3 ##

Thanks

Just curious, since we're discussing them this week in my class. Why do we need logarithms? Aren't they just a concoction to express exponents?

Homework Statement http://puu.sh/cKVxE/fb13f83a75.png In this image, I have no idea what the math behind this problem is. What exactly is happening here? Homework Equations The Attempt at a Solution I multiplied n/10 in order to get 10000n^9 as a denominator but the ln(2) confuses me...

Let us define the following $$I(n,m) = \int^1_0 \log^n(x)\log^m(1-x)\,dx$$ Our purpose is finding a closed form for the general case. Note: for a given n and m the above formula can be deduced by succesive differentiation of the beta representation $$B(p,q) = \int^1_0 x^{p-1}...

Homework Statement y= -2log3(x-3) -1 Homework Equations I am using a SHARP EL-546W scientific calculator, and I do not know what steps to take in order to find a point given an x value. i.e. if x=3, then y=6. I cannot seem to get 6 on my own and I have tried a wide variety of methods and...

Hey! I have a question regarding a statement in my physics book. I don't see how |H(f)|_{dB} = - 10log (1+( \frac{f}{f_B})^2) approaches this equation below for big values on f. |H(f)|_{dB} = - 20log ( \frac{f}{f_B}) Could you please help me out? Thanks in advance. EDIT: I am sorry if...

How do I work out how many times more acidic a ph value of 6.8 is compared to 8.6? For example.

Homework Statement Show that ^{2}log(e)=\frac{1}{ln2} Homework Equations ^{a}log(x) = ^{a}log(b)\cdot ^{b}log(x)^{a}log(x)=\frac{^{b}log(x)}{^{b}log(a)} The Attempt at a Solution How can this be shown? I assume it can be done just using logarithm laws, but I don't see how. I tried manipulating...

Express as a Single Logarithm. Assume all the logarithms have the same base. The problem is: $4*\log_{d}\left({a}\right)-\frac{5}{6}*\log_{d}\left({b}\right)+\frac{2}{3}*\log_{d}\left({c}\right)$, where $d\gt1$ then I use the power rule for logarithm for the beginning and use some grouping...

I am attempting to write a page concerning exponentiation and logarithms for my website www.1728.com Basically I'd like to know the precise terminology. In the equation 2³ = 8 we can say that "2" is the base, "3" is the exponent but what exactly is the "8" called? I have seen it referred...

Homework Statement Calculate the value of y in the expression below: 10y = 103.2 × 102.4 × 10-1.8 × 1000.3 × 100-0.5 Homework Equations The Attempt at a Solution 10y= 103.8*100-0.2 Don't know how to move on from here as have no other examples like it? I am thinking I can use logs, however...

Hello, I am beginning to learn precalculus. I understand that there are times where you can change logarithms to exponential expressions. So how are they different and similar and why are they interchangeable?

I'm getting myself all confused with complex logarithms. I'll try to explain why. One identity with complex logarithms is ln(z^c)=cln(z)+2πik, with k an integer. This is, of course, a more general case of ln(e^c)=c+2πik, but it doesn't always work the same! Let's say we are evaluating ln(e^i)...

Hey there! How do I determine whether this function is growing or decreasing without using any calculator or graphing tools? y=ln(\frac{1}{x}) I know that y=ln(\frac{1}{x}) \ \Leftrightarrow \ e^y=\frac{1}{x} \ \ \ (1) Then I tried to use the formula f(x)=a^x and then determine whether...

Use the properties of Logarithms to write the expression as a sum, difference, and/or constant multiple of logarithms:

Alright so my problem is if I don't see exactly how things work (in math) I can't use them. Like what I mean is some people use memorization and other methods but I really need to understand things deep down to be successful. So my problem is, I have trouble understanding logarithms. Now I...

If I understand Logarithms correctly it is the orders of magnitude? Either exponentially growing or exponentially decaying. I've heard that exponential growth is the same as the growth of cancer cells. But what are some other real life applications/examples of logarithms? Thank You

Homework Statement A geometric series has first term and common ratio both equal to ##a##, where ##a>1## Given that the sum of the first 12 terms is 28 times the sum of the first 6 terms, find the exact value of a. Hence, evaluate log_{3}(\frac{3}{2} a^{2}+ a^{4}+...+ a^{58}) Giving...

Hello, I have been studying Logarithms in University. I understand it's how many of ONE number to get another number, and I see how it is rearranged to find these "missing" links. But maybe I am overlooking something, but I don't quite see the bigger picture here with how to use Logarithms. How...

Homework Statement If y= 10^x, show by taking logarithms to base e that y = exln10 Homework Equations The Attempt at a Solution Well what I did was y= 10^x so ln y = xln10 they told me that y = exln10 so ln y = xln 10 , so ln y = lny so y = y so y= 10^x. The way I...

Homework Statement Log(2x-3)=log(4x-3)-logx Homework Equations Logcl =logcr L=r The Attempt at a Solution Quotient law of logs So I simplfied: Log(2x-3)=log(4x-3)/x Since same base: 2x-3=4x-3/x 2x^2-7x+3=0 (X-1)(x-6) The ans is supposed to be 3. I don't know what I'm doing wrong?

Homework Statement 2^{3x} = 7^{x+1} Homework Equations N/A The Attempt at a Solution 2^{3x} = 7^{x+1} I'm not entirely sure how to proceed from here. I'm assuming that the following is the right step towards the solution... (log2)(3x) = log(7)(x+1) ...but I'm not...

I know that in logarithms we can not set as base a negative number,but look at this(in the brackets I will put the base.): log(-2)-8=3 Mathematics say that is wrong,but why? If we tell -2^3=-8 we have a correct result. So? Thank you!

I don't have a single homework question but a general one that will help me out tonight. I am taking calculus one college level and we are reviewing logarithms and I am really having trouble. I just don't understand how we are supposed to know where to add and cancel them. It seems that at...

Greetings, This question makes reference to the stat mech book, “Fundamentals of Statistical and Thermal Physics”, by Reif, so people who have that book will probably understand where I am coming from most easily. However, the main points/questions of this post are independent of the book, so...

I read that logb x exists only when x >= 0 what about log-3 -27 though? The answer should be the exponent 3, right? Thanks!

Does anyone know if the following is true: logb (x + y) = logb x + logb y Thanks. This isn't homework, but I am just wondering if the following is true. I already know the logarithm product, quotient, and power rules!

Homework Statement If a solution containing a heavy concentration of hydrogen ions(i.e., a strong acid) is diluted with an equal volume of water, by approximately how much is its pH changed? (Express (pH)diluted in terms of (pH)original.) Homework Equations I think the question...

I'm having trouble understanding the last two lines of a recurrence relation: 2(log2 n) + kn = n + log2 n * n I get the rest of the recurrence relation, but I don't understand how those two became equivalent. Where did k go? Where did + n come from? and what happened to the 2? Here is...

so i want to study logarithms this summer , i'd like you guys to recomonned for me a good book or site i used to go to this one http://tutorial.math.lamar.edu/download.aspx it really helped me understand calculus I but they really lack info on logs , thanks in advance.

ln(a * b) = ln(a) + ln(b) and ln(a/b) = ln(a) - ln(b) correct?

Hi, So I'm doing boltzmann's entropy hypothesis. I have a basic question about the mathematics of logarithms. For \frac{ΔS}{K_B}=ln(W_f)-ln(W_i), I do the correct maths and go \frac{ΔS}{K_B}=ln(\frac{W_f}{W_i}), and finally take the log of the equation to get...

The math behind the logarithms isn't hard especially if you can remember where things go and how the math is worked out but what are they for? What do they do and why are they used? Maybe I am missing what they are used for in the math but it really just doesn't make sense. You have a base...

If I have ln(e^(-8.336/10c)) wouldn't that be the same as ln(e^(1/(8.336/10c))) therefore = 1/(8.336/10c) = 10c/8.336? I am confused about this because in my lecture notes they simplified ln(e^(-8.336/10c)) to just = -8.336/10c :confused: Your help would be appreciated!

For some polynomial functions it is useful to logarithmize both sides of the eq. First. How can this be applied for inverse trig functions? Is it even possible?

Homework Statement I'm trying to find the value of a variable which happens to be an exponent. Homework Equations 230,000=1500\frac{(1+.00077)^n-1}{.00077} I believe I need to use logarithms to get to my answer, but I've reviewed logarithm rules and I'm stuck. The Attempt at a...

What is the analytical method for solving log. eqs., like x=2^x/14 ? In high school they only teach us the graphical approach =/ joo

Homework Statement Consider the system... y=e^{-x}+1 \\ y=2+lnx The Attempt at a Solution I don't think there is a "pretty way" (algebraic manipulation) to do this. I simply found the point where the plots intercepted, getting the solution set (0.62745018..., 1.5339409...). Is there a...

Homework Statement \frac{2^{x+1}-3}{2^{x}-4}\leq1 Homework Equations The Attempt at a Solution When I go through it, I keep getting 2^{x}\leq-1 I don't think the answer is suppose to be complex... let me show you my work in a file. It's extremely embarrassing that I don't...

Homework Statement Show that the following expression is true: 0.2*0.8 = -14dB + (-1.94dB) Homework Equations 1 dB = 10log10(x) (where x is a ratio of two quantities) 10log10(ab) = 10log10(a) + 10log10(b) The Attempt at a Solution 0.2*0.8 = -14dB + (-1.94dB) 0.16...