Build Your Logarithms Skills with Engaging Lessons and Exercises

Equation $\log (x^{2} + 2 a x) = \log (4 x - 4 a - 13)$ has only one solution; then exhaustive set of values of $a$ is

Pablo Dennis 2022-04-05

Doubt on Logarithms multiplication
today I'm in doubt on calculating the follow expression $\log_{4} 3 \cdot \log_{9} 32$
Changing all to base 4: Working on: $\log_{4} 3 \cdot \frac{\log_{4} 32}{\log_{4} 9}$
Ending with: $\log_{4} 3 \cdot \frac{2 + \log_{4} 2}{2 \cdot \log_{4} 3}$
There's a way to simplify it more ? Also, do you know any resource explaining more on rules on every kind of operation with logs ?
Thanks in advance

Marzadri9lyy 2022-04-05

Does $\log_{b} (x) = \log_{b} (y) \to x = y$ ?

kazue72949lard 2022-04-05

Express in terms of logarithms of x, y, z, or w.
$\log_{4} (x z)$

Harley Ayers 2022-04-04

Equation with Logarithm:
$\log_{x} 3 + \log_{x} 12 = 2$
How do I solve it? My idea was to use the formula $\log_{a} (b) = \frac{\ln b}{\ln a}$ but that does not seem to help here.

David Rodgers 2022-04-03

Evaluate the expression without using a calculator.
$e^{2 \ln 7}$

Averie Ferguson 2022-04-03

Does the logistic function uniquely satisfy these three conditions?
Given
$r (t) = \frac{f (t)}{1 - F (t)}$ {Eq. 1}
where
$f (t) = \frac{d F}{d t}$ {Eq. 2}
and the conditions:
$lim_{t \to \infty} r (t) = 1$ {Eq. 3}
$lim_{t \to \infty} F (t) = 1$ {Eq. 4}
$lim_{t \to \infty} f (t) = 1 - F (t)$ {Eq. 5}
I can think of just one function F satisfying these three conditions--the logistic function:
$F (t) = \frac{1}{1 + e^{- t}}$ {Eq. 6}
(which can also be expressed $F (t) = r (t)$ )
Is this is the only function satisfying these conditions? If so, is there a way to prove it?

blestimd4pz 2022-04-03

Stuck on a log equation
I am having trouble figuring out how I can solve this log:
$6 \log (x^{2} + 1) - x = 0$
The steps i've thought to take so far are as follows:
step 1: subtract the right most x to the other side of the equation:
$6 \log (x^{2} + 1) = x$
step 2: divide by 6:
$\log (x^{2} + 1) = \frac{x}{6}$
step 3: make both sides an exponent of 10 to get rid of the log:
$x^{2} + 1 = 10^{\frac{x}{6}}$
step 4. ??????????????

sexoagotadorogyr 2022-04-03

State domain, range, vertical asymptote and $x, y$ intercepts for $\log_{4} (x - 1) + 1$

Rex Maxwell 2022-04-03

Solving $x^{\log (x)} = \frac{x^{3}}{100}$
How do I find the solution to:
$x^{\log (x)} = \frac{x^{3}}{100}$
So I multiplied 100 both sides getting:
$100 x^{\log (x)} = x^{3}$
Now what should I do?

Aleah Choi 2022-04-03

Solving equation $\log_{y} (\log_{y} (x)) = \log_{n} (x)$ for n
I'm just wondering, if I log a constant twice with the same base y,
$\log_{y} (\log_{y} (x)) = \log_{n} (x)$
Can it be equivalent to logging the same constant with base n? If yes, what is variable n equivalent to?

markush35q 2022-04-03

Solving an exponential equation
Alright, here's the equation:
$‎ {1.08}^{x} = {1.10}^{x - 1}$
I know I need to use logarithms, but I can't figure how to do it. Thanks in advance!

siliciooy0j 2022-04-02

Find all real solutions to the equation $3^{1 + 2 \log_{3} (y - x)} = 48$
With this problem I have difficulty getting rid of the exponent.
$2 \log_{5} (2 y - x - 12) = \log_{5} (y - x) + \log_{5} (y + x)$

Guadalupe Glass 2022-04-02

Exponential and logarithmic series: Find the sum of
$2^{2} + \frac{3^{2}}{2}! + \frac{4^{2}}{3}! + \dots$ to infinity

palmantkf4u 2022-04-02

Evaluate expression using change of base
This is an awkward question to me, it was not covered in class.
Suppose:
$\log_{b} 2 = A$
$\log_{b} 3 = B,$
$\log_{b} 5 = C$
Then, use the change-of-base formula to evaluate
$\log_{b^{2}} 5$
and
$\log_{\sqrt{b}} 2 .$
As an example answer, we're given $\log_{3} b$ becomes $\frac{1}{B}$
Hopefully someone understands where they're coming from.

ideklaraz7xz 2022-04-02

Equation with Logarithm
I want to solve the following equation:
$3^{x} 3^{x - 1} = 243 .$
My approach is the following:
$3^{2 x - 1} = 243$ then
$(2 x - 1) \cdot \log 3 = \log 243$ and then:
$x = \frac{\frac{\log 243}{\log 3} + 1}{2}$
Is this correct?

jermandcryspza3 2022-04-02

Suppose that $G (x) = \log_{3} (2 x + 1) - 2 .$
(a) What is the domain of $G$ ?
(b) What is $G (40)$ ? What point is on the graph of $G$ ?
(c) If $G (x) = 3$ , what is x? What point is on the graph of $G$ ?
(d) What is the zero of $G$ ?

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