All Questions
27
questions
0
votes
0
answers
134
views
Solve the system of equations.
There was a mistake in the previous question but it is now fixed:
$\log_{10}\dfrac{1}{3}(y + 2) \to \log_{\frac{1}{3}}(y + 2)$
Solve the system of equations for $z\ge0$: $\left\{ {\begin{array}{*{20}{...
- 449
0
votes
6
answers
80
views
Evaluating $\log_{ab} \left(\frac{x^2\sqrt[3]{a}}{bc^3}\right)$, given the values of $\log_xa$, $\log_xb$, $\log_xc$ [closed]
I am totally drawing a blank on how you would go about solving this.
Let's say you have the following equations:
$$\begin{align}\log_x a &= 4.22 \\
\log_x b &= 3.7 \\
\log_x c &= 2.41
\...
- 101
2
votes
2
answers
121
views
$a = \log_{40}100, b = \log_{10}20$.How can I express $b$ depending only on $a$?
Let $a = \log_{40}{100}, b = \log_{10}{20}$. How can I express $b$ depending only on $a$? I tried using the formula to change the base from $40$ to $10$, but couldn't get it just depending on $a$.
I ...
- 95
2
votes
1
answer
61
views
System of logarithmic and exponential equations $\log_{7}(x^2-x+1)=\log_{2}(y^2-1)-\log_{2}(x+1)$
Solve the following system in $\mathbb{R}$.
$$\log_{7}(x^2-x+1)=\log_{2}(y^2-1)-\log_{2}(x+1)$$
$$\log_{7}(y^2-y+1)=\log_{2}(z^2-1)-\log_{2}(y+1)$$
$$\log_{7}(z^2-z+1)=\log_{2}(x^2-1)-\log_{2}(z+1)$...
- 187
0
votes
2
answers
68
views
Solving for $x$ in the equation $xa^x = y$
I am trying to solve the equation
$$xa^x = y,$$
for $x$ where $x$ should be positive.
The only thing known is $a < 1$. I tried taking logarithm of both side but it doesn't really lead anywhere.
- 691
3
votes
0
answers
83
views
How can I solve a system of 3 equations that use logs?
I'm having a bit of trouble solving this system of equations. What would be a good way of solving for the three variables in a question like this? I've tried many different ways of substituting or ...
- 31
1
vote
1
answer
48
views
Can $\frac{x-c}{x} = \frac{y-c}{y}e^{-\frac{(x/y)-1}{(x/y)+1}}$ be solved explicitly for $x$ and $y$
where $c>0$ and $x,y \geq 0$.
Is there an explicit way (closed form) to solve the equation in the title?
I believe the answer is that it must be that $x=y$, at least according to my logic below, ...
- 975
0
votes
1
answer
55
views
Solve the system of equations with exponential term.
I am trying to solve this system of equations. I know the answer but I am struggling with the working. I need to solve for $m$ and $s^2$ in terms of all the other parameters. The system of equations ...
user671338
0
votes
5
answers
130
views
What is $\log_{a}{x} \cdot \log_{y}{a}$ given below system of equations?
I let $\log_{a}{x}=m$ and $\log_{y}{a}=n$. So I have to find $m\cdot n$. From the system of equations we get
$$m-\frac{1}{n}=1 \quad \quad n-\frac{1}{m}=1$$
From here I find that $m=n$ (...
- 758
1
vote
3
answers
123
views
Complicated System of Equations involving Logarithms
I am trying to solve this system of equations. I know the answer but I am struggling with the working. I need to find $x$, $y$, and $z$ in terms of $a$, $b$, and $c$.
The system of equations is shown ...
- 195
4
votes
3
answers
287
views
Exponential/Logarithmic equation system
Solve the following equation system over the real numbers
$$\begin{cases}
x(1-\log_{10}(5))=\log_{10}(11-3^y)\\
\log_{10}(35-4^x)=y\log_{10}(9) \\
\end{cases}
$$
For the functions in the above ...
- 283
2
votes
1
answer
409
views
Solution for Simultaneous Logarithmic Equations
Following are the Equations:
\begin{align}
\log x +\frac {\log(xy^8)}{((\log x)^2+(\log y)^2)} &= 2 \\
\log y + \frac{\log(x^8/y)}{((\log x)^2 +(\log y)^2)} &= 0
\end{align}
I tried ...
- 29
2
votes
2
answers
109
views
Solving $2^x=x^3$ Algebraically
How can I solve $2^x=x^3$ algebraically?
I could take $\log_2(\cdot)$ on both sides, but I'd still be stuck.
- 83
2
votes
2
answers
71
views
Calculating multiple parameters for a logarithmic function
I have the following function -
$$y=\ln(Ax^D+B+Cx^E)$$
These are the coordinates:
$$(1, 1)$$$$(2, 0.84)$$$$(4, 1.5)$$$$(31, 4.1)$$$$(44, 5)$$
How can you solve this equation and what is the ...
- 155
0
votes
3
answers
52
views
Help with simple logarithmic system of equations [closed]
It's simple, I just need a little bit of help to get started.
$$\log_yx-\log_xy=\frac{8}{3}$$
$$xy=16$$
- 1,759