Build Your Logarithms Skills with Engaging Lessons and Exercises

solving equations with powers
Im trying to solve the equation
$3 \cdot 2^{- 2 / x} + 2 \cdot 9^{- 1 / x} = 5 \cdot 6^{- 1 / x}$
So far I tried applying logaritmas but it didnt prove helpful...are there any other ways?

flatantsmu 2022-09-06

Solving $F (x) = 0.3$ where $F (x) = 1 - \frac{200^{2.5}}{x^{2.5}}$
Consider the function
$F (x) = 1 - \frac{200^{2.5}}{x^{2.5}} .$
We want to solve $F (x) = 0.3$
1.Since $F (x) = 0.3$ then we can say, $2.5 \ln (\frac{200}{x}) = 0.7$
2. $\ln (\frac{200}{x}) = 0 .28$
3. $e^{\ln (\frac{200}{x})} = e^{.28}$
4. $\frac{200}{x} = e^{.28}$
5.Hence $x = \frac{200}{e^{.28}}$
6.The answer appears to be about $x = 151.16$
Just to sum it up, the actual answer is $230.66$ , and this was achieved by taking the 2.5th root instead of doing the natural log. Why wasn't it the same answer?

Sanai Ball 2022-09-06

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. $\log_{\frac{1}{3}} 71$

clovnerie0q 2022-09-06

If $\log_{2} 3 = a$ and $\log_{5} 2 = b$ then $\log_{24} 50$ is equal to?
I guess this has to be done by using simple logarithmic rules, but I do not how to start. Answer in my booklet is $\frac{b + 2}{b (a + 3)}$

Bridger Holden 2022-09-06

properties of logarithms $\ln 12 - \ln 2 = \ln 6$
I checked wolframalpha and it says that ln12-ln2=ln6. How? i tried to do: ln12=ln(223) which may be 2ln(2*3) (which is probably wrong). I need help.
EDIT: Ok, thanks. Actually i could have just searched logarithms properties on google(didn't think about it). Sorry for taking your time.

flatantsmu 2022-09-06

Find the solution set of the equation
$\log_{x} (3 x - 2) + \log_{x^{2}} (\frac{1}{3 x - 2}) = 1$

jhenezhubby01ff 2022-09-06

How to prove $\ln x < x$ ?
How can we prove that the inequality
$\ln x < x$
It is trivial in the cases $0 < x \leq 1$ . I couldn't do anything for $x > 1$

Sasha Hess 2022-09-05

Find the last three digits of the product of the positive roots of $\sqrt{1995} x^{\log_{1995} x} = x^{2}$

equipokypip1 2022-09-05

Evaluate. $\ln \sqrt{x + 2} = 1$

treallt5 2022-09-05

The mass m (t) remaining after t days from a 40 gram sample of thourium-234 is given by $m (t) = 40 e^{- 0.0277 t}$ . What is the half-life of thorium-234?

Brodie Beck 2022-09-05

How do I calculate the limit of this log function?
I've been stuck with calculating the limit of the following problem for a while now. Can you help?
$lim_{x \to \infty} \frac{\sqrt{\log (x) + 1}}{\log (\log (x))} =$

hazbijav6 2022-09-04

find the value of $k$ in the term $2^{- k} = 1 / n$
What is the value of $k$ if I have the following equation: $2^{- k} = \frac{1}{n}$ ?
$2^{- k} = \frac{1}{n} ⟹ n = 2^{k} ⟹ \log_{2} n = k$
Is my solution correct?

Tia English 2022-09-04

Which is more preferable to write $\log (x)$ or $\ln (x)$
Which one is more preferable to write when you are writing an exam. Is it $\log (x)$ which denotes the natural logarithm or is it $\ln (x) .$

decorraj9 2022-09-04

Evaluate. $\frac{400}{1 + e^{- x}} = 350$

Jocelyn Bernard 2022-09-04

If $f (x) = x^{x} \ln (5 x - 5)$ , and $f^{'} (x) = x^{x} \ln (5 x - 5) (g (x))$ , Then What Would g(x) Equal?

Kassandra Mccall 2022-09-04

What is the solution to the equation $9^{x} - 6^{x} - 2 \cdot 4^{x} = 0$ ?
I want to solve:
$9^{x} - 6^{x} - 2 \cdot 4^{x} = 0$
I was able to get to the equation below by substituting $a$ for $3^{x}$ and $b$ for $2^{x}$ :
$a^{2} - a b - 2 b^{2} = 0$
And then I tried
$\begin{aligned} x & = \log_{3} a \\ x & = \log_{2} b \\ \log_{3} a & = \log_{2} b \end{aligned}$
But I don't know what to do after this point. Any help is appreciated.

st3he1d0t 2022-09-04

Logarithm problem with two bases
Given
$\log_{x} 9 + \log_{9} x = \frac{10}{3} .$
How can I find the greatest value of x that satisfies the equation above?

fofopausiomiava 2022-09-04

Write the expression in terms of $\log x$ and $\log y$
$\log (\frac{x^{3}}{10 y})$
To be honest, I'm really unsure as to how the final answer should look like. In other words, what is the question asking for, and how do I go about getting there?
Any ideas would be appreciated.

tashiiexb0o5c 2022-09-04

Find the smallest positive integer k such that the baseten representation of 3k has exactly one hundred digits.
If $\log_{8} 3 = p a n d \log_{3} 5 = q$ , then, in terms of p and q, $\log 5$ equals to?

Elena Simmons 2022-09-04

Rewrite as a single log with a coefficient of one.
$(4 \ln (x)) - (3 \ln (x)) + (1 / 4 \ln (x))$

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