Build Your Logarithms Skills with Engaging Lessons and Exercises

Steps to calculate $\log_{2} 0.667$
This could be a basic question. But I would like to know steps I should follow to calculate $\log_{2} 0.667$

Lucian Ayers 2022-04-02

Solving $8 n^{2} = 64 n \log (n)$

Zoie Phillips 2022-04-02

Rewrite as a sum of logarithms using the Product Rule of Logarithms
$\log (8 x)$

Zoie Phillips 2022-04-02

Proof of the fact that $\ln (a) = f^{'} (0)$ for $f (x) = a^{x}$ ?

Petrolovujhm 2022-04-02

Proof of a closed form of $\int_{0}^{1} {(- \ln x)}^{n} d x$

Aryan Salinas 2022-04-01

Solving an equation with a logarithm in the exponent
I try to solve the following equation:
${(N + 1)}^{\log_{N} 125} = 216$
I know the answer is 5 here but how could I rewrite the equations so I can solve it?
I tried to take the log of both sides but that didn't help me because I got stuck. Could anyone please explain me how to do this?
Thanks!

encaderpwp 2022-04-01

How to solve
$5 - \log_{2} (x - 3) = \log_{2} (x + 1)$

Oliver Tyler 2022-04-01

How to solve a literal equation
How do I solve $2^{x - 1} = 3^{x + a}$ I cannot solve it and have spent an hour on it trying many different ways. Please help me! Thank you!

xxgetthisar08 2022-04-01

How to solve
$\frac{(3 \log_{y} 5) (2 \log_{y} 5)}{(6 \log_{y} 5)}$ ?

Jaylin Clements 2022-04-01

Proof the logaritmic identity
Please help me proving the basic logarithmic identity
$\log_{3} 12 = 1 + \log_{5} 4 \cdot \log_{6} 5 \cdot \log_{3} 6$

Milton Robertson 2022-03-31

Solving the following equation:
$2^{x} + \log_{10} x - 2 = 0$

svrstanojpkqx 2022-03-31

Solving $1 + x^{10 + {\log x}^{10 + {\log x}^{10 + \dots}}} = \frac{1}{\log x}$
To solve this equation I used $t = 1 + x^{10 + {\log x}^{10 + {\log x}^{10 + \dots}}}$ . LHS is equal to,
$1 + t = 1 + x^{10 + \log t}$
$t = x^{10 + \log t}$
$\log t = (\log x) \times (10 + \log t)$
$x = e^{\frac{\log t}{10 + \log t}}$
Hence the equation is equivalent to
$t + 1 = \frac{10 + \log t}{\log t}$
$t \log t = 10$
I'm not sure if this helps in solving the equation.

Alexis Alexander 2022-03-31

$\log_{5} {- 3} = \frac{\log (3) + π i}{\log (5)}$ ?

nomadzkia0re 2022-03-31

Proving Logarithmic identity
Today, I read these two new Logarithmic identity
$a^{\log_{a} m} = m$
$\log_{a^{q}} m^{p} = \frac{p}{q} \log_{a} m$
Both of them seems new to me,so even after solving some problems (directly) based on thesm I haven't fully understood how they holds good,Could anybody show me how to prove them ?

Jazmyn Holden 2022-03-31

Prove $\log_{10} (2)$ is irrational

Samuel Herrera Liberato2022-03-30

aanvarendbq28 2022-03-30

I am new to logarithms and I am having trouble with this logarithm system.
$\log_{9} (x) + \log_{y} (8) = 2$
$\log_{x} (9) + \log_{8} (y) = \frac{8}{3}$
A step-by-step procedure would be highly appreciated.
Thanks in advance.

Nancy Richmond 2022-03-30

How would I evaluate
$y = e^{2 \frac{\ln 2}{3}} + e^{- \frac{\ln 2}{3}} ?$

peggyleuwpodg 2022-03-30

How to solve exponential function of form $a b^{x} + x = c$ ?
For instance, how would I solve: $3^{x} + x = 85$ ?

ropowiec2gkc 2022-03-30

Proving the limit of $\frac{{\log (n)}^{\log (n)}}{{1.01}^{n}}$
Can anyone please show me a simple way (if there is one) to show that
$lim_{n \to \infty} \frac{{\log (n)}^{\log (n)}}{{1.01}^{n}} = 0$
And that
$lim_{n \to \infty} \frac{{1.01}^{n}}{n!} = 0$
I've checked that it's true, I just need to show it the shortest way possible.

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