All Questions
23
questions
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.
$$
x = \frac{\sqrt[3]{(23.57^2 - 15.63^2)}}{{0....
2
votes
2
answers
648
views
What is wrong with my approach to solving $x^{\log25} + 25^{\log x} = 10\;$?
Found this equation on the web: $$x^{\log25} + 25^{\log x} = 10$$
The person solved by substitution and got $x = \sqrt{10}$ which satisfies the equation.
I tried different ways after following the man'...
- 119
0
votes
0
answers
30
views
What if a point in $[a,b]$ does not lie in the domain of $f(x)$ while applying IVT
I came across the function $f(x)=x^3\ln(\sin x)$. I tried applying IVT in the interval $\left[-\frac{5 \pi}{4},-\pi\right) \cup\left(0, \frac{3 \pi}{4}\right]$.
Now we see that
$$\begin{aligned}
f\...
- 10.2k
1
vote
2
answers
82
views
Why does $e^{t+4}(t-1)=0$ only yield one solution?
I understand that $e^{t+4}(t-1)=0$ only yields one solution because $e^x >0$ what I am wondering is why you can't $\ln$ to cancel out the $e$ to give $(t+4)(t-1)=0$
This is clearly invalid from ...
- 11
0
votes
1
answer
130
views
Restrictions on exponent laws
Alright, so i want to add restrictions to this list of exponent laws. The code i will post now is my attempt at writing their restrictions and the laws i want to write restrictions on. SO, please let ...
- 77
-2
votes
1
answer
202
views
How to solve the equation $\log_5x+\log(x+1)=\frac{\log12}{1-\log2}$? [closed]
How can one solve the equation: $$\log_5x+\log(x+1)=\frac{\log12}{1-\log2}$$
- 117
2
votes
6
answers
384
views
Show that $f(x)$ is an Odd Function
Show that $$f(x) = \ln \left(x+\sqrt{x^2+1}\right)$$ is an odd function.
My attempt:
$$f(-x)=\ln\left(-x+\sqrt{(-x)^2+1}\right)=\ln\left(-x+\sqrt{x^2+1}\right).$$
How should I proceed? I know that ...
- 7,788
1
vote
2
answers
130
views
logarithmic equation $\log_2(3^x-8)=2-x$
I've been unable to solve the following equation:
$$\log_2(3^x-8)=2-x$$
I can arrive at $$3^x-8=2^{2-x}$$ but I'm clueless afterwards. I know that the answer is $x=2$ but cannot arrive to that ...
- 49
2
votes
1
answer
113
views
Solve an equation with the form $y=\left(1+\frac{a}{x}\right)^{bx}+c$
Knowing that $\lim_{x\to \infty}\left(1+\frac{1}{x}\right)^x=e$
and, $\lim_{x\to \infty}\left(1+\frac{a}{x}\right)^{bx}=e^{ab}$
and also, $\lim_{x\to \infty}\left[\left(1+\frac{a}{x}\right)^{bx}+c\...
- 59
1
vote
0
answers
281
views
Removing exponent from equation
I'm trying to solve the following equation numerically:
This is problematic, because the term $ t^{\beta_i}_{j} $ becomes extremely large ($> 10000^{300}$), and unrepresentable with typical number ...
- 111
3
votes
2
answers
264
views
Solving for $x$ : $a^x+b^x=c$
Well the question is to solve for $x$ in $$a^x+b^x=c \tag{a,b,c are constants}$$
Well as of me, I tried to put $\ln{}$ on both sides which does not seem to help. Apart from this I don't seem to have ...
- 2,221
6
votes
4
answers
996
views
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 $2^x$:
$$ a^2 - ab - 2b^2 = 0 $$
And then I tried
\begin{align}x ...
- 219
0
votes
2
answers
46
views
Solving for $x$ using $\ln$ or any possible way.
$$
12.46x=1-(1+x)^{-20}
$$
I tried solving for $x$ using $\ln$ and other methods but the only answer i got was 0.8.
The correct answer is approximately to $0.05$.
6
votes
1
answer
160
views
How to solve the equation $ (x-2)^{\log_{100}(x-2)}+\log_{10}(x-2)^5-12 = 10^{2\log_{10}(x-2)}$?
If $\displaystyle (x-2)^{\log_{10^2}(x-2)}+\log_{10}(x-2)^5-12 = 10^{2.\log_{10}(x-2)}$, then value of $x$ is ...
My Try
Let$$\log_{10}(x-2) = y \quad \Leftrightarrow \quad (x-2)=10^y .$$
Then$$(10)^{...
- 53.7k
2
votes
2
answers
111
views
What is wrong with this solution?
$$ \ln(x) = 1 + \ln(5)$$
$$ x = e^{1+ \ln(5)} = e^{1+5} = e^6$$
What exactly am I doing wrong here?
- 2,047