All Questions
Tagged with algebra-precalculus logarithms
1,541
questions
1
vote
3
answers
115
views
How to solve $x+1=5e^{4x}$ [closed]
How to solve $x+1=5e^{4x}$
In general, I know to take ln() of both sides to bring down the exponent for e, but the left side is also a variable.
- 4,771
0
votes
1
answer
53
views
Solving a logarithmic equation with different logarithmic exponents.
I had a logarithmic equation which originally was
original
https://i.sstatic.net/2fSf1jNM.png
$$5^{\log_{10}x}-3^{\log_{10}x-1}=3^{\log_{10}x+1}-5^{\log_{10}x-1}$$
but I thought that this should also ...
3
votes
2
answers
77
views
How to evaluate an expression of higher powers and roots using logarithms?
I am struggling with the following question from a Dutch algebra exam from the 1950s. The instructions are as follows:
Calculate with logarithms.
$$
x = \frac{\sqrt[3]{(23.57^2 - 15.63^2)}}{{0....
-2
votes
1
answer
59
views
How does $\log(y)=C+t$ become $y = C e^{t}$? [closed]
I came across this transformation :
$$\begin{align}
\log(y) &= C + t \tag{1} \\[4pt]
y &= C e^{t} \tag{2}
\end{align}$$
How was the first step simplified into the second?
- 7
0
votes
2
answers
69
views
Suppose a colony of cells starts with 10 cells, and their number triples every hour. After how many hours will there be 500 cells?
I thought it would be log(500), which gives approximately 2.69897. I know that there could be alternative forms of the answer, but for the life of me, I don't understand how they arrive at this ...
- 83
0
votes
1
answer
20
views
Question regarding finding the rate of depreciation in a half-life equation. This uses logarithms but I am unsure how to arrive at the answer given. [closed]
This question is from a chapter regarding logarithms. I have correctly answered part (a) of the question, which simply involves substituting the variables for the values given, so I need no help with ...
- 83
-1
votes
1
answer
27
views
A star's magnitude $M$ and intensity $I$ satisfy $M=6-2.5\log\frac{I}{I_0}$. Find the ratio of intensities between stars of magnitude $1$ and $3$. [closed]
My textbook doesn't go into how to solve this question.
The magnitude of a star is given by the equation
$$M=6-2.5\log\frac{I}{I_0}$$
where $I_0$ is the measure of the faintest star, and $I$ is the ...
- 83
10
votes
2
answers
797
views
Question regarding nature of logarithmic equations
While reading my textbook's chapter about logarithms and seeing the solved examples I noticed in various places that the author was able to make the $\log$ just disappear in a equation or inequality ...
- 356
1
vote
2
answers
30
views
Getting the domain of a real function with iterated logarithms [duplicate]
I would like to find the domain of the function
$$f(x)\:=\: \log_4\,\log_5\,\log_3\big(\,18x - x^2 - 77\,\big)$$
as a subset of $\mathbb R\,$.
I looked at the solution of the above problem, and it ...
- 356
0
votes
1
answer
68
views
Wrong simplification of $2^{\sqrt{\log_2n}}$ [duplicate]
I am trying to do the exercise 01, chapter 02 of the book: Algorithm Design [Kleinberg _ Tardos] - publication version 03 of the book
I need to manipulate $2^{\sqrt{\log_2n}}$, what I did was:
$2^{\...
1
vote
3
answers
131
views
Solve $x^2-2x+1=\log_2( \frac{x+1}{x^2+1})$
Solve in $\mathbb R$ the following equation $$x^2-2x+1=\log_2 (\frac{x+1}{x^2+1})$$
First of all from the existence conditions of the logarithm, we have $x > -1$. Analyzing $x^2 - 2x - 1$ , we get ...
- 125
0
votes
1
answer
76
views
How Can Solving $\left( 2n \right)^{\left( \log_b 2 \right)} = \left( 5n \right)^{\left( \log_b 5 \right)}$ be Generalized for any Base of $\log_b n$?
The title of the question Solving $(2n)^{\log 2}=(5n)^{\log 5}$ asks how to solve (in some western conventions) base 10 for $(2n)^{\log 2}=(5n)^{\log 5}$. However that question's title does not seem ...
- 951
0
votes
0
answers
343
views
An analytic solution to solve $x^9=3^x$
I want to find a way to solve $x^9=3^x$ analytically, for two roots. one of them can be found below $$x^9=3^x\\(x^9)^{\dfrac {1}{9x}}=(3^x)^{\dfrac {1}{9x}}\\x^ { \ \frac 1x}=3^{ \ \frac 19}\\x^ { \ \...
- 25.2k
1
vote
1
answer
90
views
Simplify $\log((10\cdot 8 )^{\frac{1}{2}} \times (0.24)^{\frac{5}{3}} \div (90)^{-2})$
Simplify $\log((10\cdot 8 )^{\frac{1}{2}} \times (0.24)^{\frac{5}{3}} \div (90)^{-2})$
$\Rightarrow \log(10\cdot 8)^{\frac{1}{2}}+\log(0.24)^{\frac{5}{3}}-\log(90)^{-2} \tag{1}$
$\Rightarrow \dfrac{1}...
1
vote
1
answer
68
views
Find the value of $\sqrt[5]{0.00000165}$ given $\log165=2.2174839$ and $\log697424=5.8434968$
Find the value of $\sqrt[5]{0.00000165}$ given $\log165=2.2174839$ and $\log697424=5.8434968$
$\log x=\log\sqrt[5]{0.00000165}$
$\Rightarrow \log x =\dfrac{1}{5}\log0.00000165=\dfrac{1}{5}(\overline{...