Build Your Logarithms Skills with Engaging Lessons and Exercises

Use the properties of logarithms to simplify the following function before computing $f^{'} (x) . f (x) = {{\ln (4 x + 3)}^{2} f}^{'} (x) =$

Kendal Day 2022-04-10

Unknown in logarithm base $\frac{122312}{100000} = {(1 + t)}^{5}$
I am new to exponents and logarithms, and have been stuck with this for a quite long time.
The problem is:
$\frac{122312}{100000} = {(1 + t)}^{5}$
or
$\log_{1 + t} \frac{122312}{100000} = 5$
I have no idea, how to solve this. Hints or tips would be very very welcomed.
Thank You (a lot) in advance!(also apologies for my poor english)

Edith Mayer 2022-04-10

Solve $2 \log_{3} (x) - \log_{3} (x + 6) = 1$
just getting going with logarithms, having trouble with this question.
$2 \log_{3} (x) - \log_{3} (x + 6) = 1$
$\log_{3} x^{2} - \log_{3} (x + 6) = 1$
Stuck at this point: What do I do next?
$\log_{3} (\frac{x^{2}}{x + 6}) = 1$
Edit: Got it!
$\frac{x^{2}}{x + 6} = 3^{1}$
$\frac{x^{2}}{x + 6} = 3$
$x^{2} = 3 (x + 6)$
$x^{2} = 3 x + 18$
$x^{2} - 3 x - 18 = 0$
$(x - 6) (x + 3) = 0$
$x = 6$ and cannot equal $\neq 3$ as $2 \log_{3} (- 3) < 0$

Jefferson Pacheco 2022-04-09

I want to simplify the following expression.
$Y = Bottom + \frac{Top - Bottom}{1 + 10^{((\log E C 50 - X))}}$
log is base of 10. Some may know that it's a dose response curve, and I want to solve for EC50.
I tried simplifying it but I forgot math long time ago and I couldn't find the answer online.
My problem was the exponential and logarithms part.
Can someone simplify the expression to solve for EC50?
Thank you very much.
Edit : And if someone could explain simplifying exponential and logarithm on this one, it would be great as well. I forgot all the math and I would appreciate it.

Alessandra Carrillo 2022-04-09

How to simplify $\frac{\log_{2} 625}{\log_{2} 125}$

Christopher Stone 2022-04-09

How to prove the inequality
$\frac{1}{n} + \frac{1}{n + 1} + \dots + \frac{1}{2 n - 1} \geq \log (2) ?$

Lisa Cooper 2022-04-09

Use identities to simplify ${\log (a^{2} + b^{2})}^{2}$
Use logarithmic identities to simply the following:
${\log (a^{2} + b^{2})}^{2}$
I started with
${\log (a^{2} + b^{2})}^{2} = 2 \cdot \log (a^{2} + b^{2})$
I think it's not the final result, but I don't know how to proceed. Any hints would be helpful.

wadiad6qxb 2022-04-09

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places, $\log_{40.863}$

Deja Vaughn 2022-04-08

I'm in doubt on simplifying the expression: $\log_{2} 6 - \log_{4} 9$
Working on it I've got: $\log_{2} 6 - \frac{\log_{2} 9}{2}$
There's anyway to simplify it more ? I'm learning logarithms now so I'm not aware of all properties and tricks.
Thanks in advance

Ekwadorkadba3 2022-04-08

How to simplify this?
$\frac{n^{\log m}}{m^{\log n}}$

Cash Duncan 2022-04-08

How to show that $- \log_{b} x = \log_{\frac{1}{b}} x$

Jasiah Vincent 2022-04-08

How to prove this ln inequality?
I have the following inequality, which (supposedly) holds for every $x \in R$
$1 + x \ln (x + \sqrt{1 + x^{2}}) \geq \sqrt{1 + x^{2}}$
I've been struggling to find some known inequalities involving logarithms that could be applied here (and lack of condition for x to be non-negative doesn't help either). I would be very helpful for hints on how this should be approached.

Freddy Novak 2022-04-08

How to prove derivative of logarithm with base $b$ ?
I learned how to derive a logarithm with any base. This is the formula:
$\frac{d}{d x} \log_{b} x = \frac{1}{x \ln b}$
How can it be proved?

Breanna Fisher 2022-04-08

Use properties of logarithms to condense the logarithmic expression . Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator.
$3 \ln x - \frac{1}{3} \ln y$

Alan Zavala 2022-04-07

Finding the coefficient of $x^{n}$ in the expansion of ${{({\log_{e} (1 + x)})}^{2}}$
I've been trying to find the coefficient of xn in the expansion of ${({\log_{e} (1 + x)})}^{2}$ .I wrote out the expansion of ${{({\log_{e} (1 + x)})}^{2}}$ explicitly and tried to generalize the terms involving $x^{n}$ , but...so far no luck.
Is there any other alternative ?

Santos Mooney 2022-04-07

Find the solution for the exponential equation in terms of logarithms. $\frac{8 x}{2} = 5^{1 - x}$

Angelina Kaufman 2022-04-07

I'm quite ashamed that I'm at a math-related course at the university and I'm stuck. I can't solve at all this equation:
$n = 8 \log_{2} (n) .$
I have tried applying the log property so it becomes $2^{n} = 2^{8 n}$
Besides that this didn't help me, I'm not even sure if I applied right the property that says $x = \log_{2} (y) \Rightarrow 2^{x} = y$
Thanks in advance! Best Regards,

Quinn Moses 2022-04-06

How to show negative entropy function $f (x) = x \log (x)$ is strongly convex?

Aliana Alvarez 2022-04-05

Finding the intersections between $y = e^{x}$ and $y = x + 2$ algebraically?

Marzadri9lyy 2022-04-05

Evaluating a limit with variable in the exponent
For $lim_{x \to \infty} {(1 - \frac{2}{x})}^{\frac{x}{2}}$
I have to use the L'Hospital"s rule, right? So I get:
$lim_{x \to \infty} \frac{x}{2} \log (1 - \frac{2}{x})$
And what now? I need to take the derivative of the log, is it: $\frac{1}{1 - \frac{2}{x}}$ but since there is x, I need to use the chain rule multiply by the derivative of $\frac{x}{2}$ ?

Finding logarithms questions and answers online is always pure luck, especially if these are provided with detailed answers to questions. This is exactly what you can find below regardless of your practical application, college course, or complexity. These logarithms questions are related to higher education courses, which is why they will help you find the answers to what you currently have. When you deal with logarithmic equations you are approaching an exponential equation where the variable appears in an exponent as it’s in (log b (bx) = x. It also shows that the logarithmic graph equation can be represented as well.

Algebra II

Learn How to Graph Logarithmic Equations