Solve ${e}^{x}=2$

Marla Payton
2021-12-13
Answered

Solve ${e}^{x}=2$

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Pansdorfp6

Answered 2021-12-14
Author has **27** answers

Thomas Nickerson

Answered 2021-12-15
Author has **32** answers

asked 2022-07-15

This is a question in our book, and the answer in the teacher's book is "No", and a friend of mine says that their teacher also says that a rational function always has a definite $n$ number of docontinuity points.

But I can think of a few functions that have an infinite number of discontinuity points;

1) $f(x)=\frac{1}{\mathrm{sin}x}$ which is discontinuous at every $x$ value that satisfies $x=n\pi $ where $n$ is an integer. The same is also true for this function but with cosine and tan and their respective infinite sets of discontinuity points

2) $f(x)=\frac{1}{\sqrt{{r}^{2}-{x}^{2}}}$ which is discontinuous over the whole interval $[-r,r]$ and has an infinte number of discontinuity points that belong to this interval

Now I think I'm wrong here because I'm not sure if these count as "rational functions" or not.

But I can think of a few functions that have an infinite number of discontinuity points;

1) $f(x)=\frac{1}{\mathrm{sin}x}$ which is discontinuous at every $x$ value that satisfies $x=n\pi $ where $n$ is an integer. The same is also true for this function but with cosine and tan and their respective infinite sets of discontinuity points

2) $f(x)=\frac{1}{\sqrt{{r}^{2}-{x}^{2}}}$ which is discontinuous over the whole interval $[-r,r]$ and has an infinte number of discontinuity points that belong to this interval

Now I think I'm wrong here because I'm not sure if these count as "rational functions" or not.

asked 2022-03-07

Write each expression as a sum and/or difference of logarithms.Express powers as factors.

$\mathrm{ln}\frac{5x\sqrt{1+3x}}{{(x-4)}^{3}},x>4$

asked 2022-02-11

How do you multiply (4n+1)(2n+6)?

asked 2020-11-01

Given the following function:
$f\left(x\right)=1.01{e}^{4x}-4.62{e}^{3x}-3.11{e}^{2x}+12.2{e}^{x}-1.99$
a)Use three-digit rounding frithmetic, the assumption that ${e}^{1.53}=4.62$ , and the fact that $e}^{nx}={\left({e}^{x}\right)}^{n$ to evaluate $f\left(1.53\right)$
b)Redo the same calculation by first rewriting the equation using the polynomial factoring technique
c)Calculate the percentage relative errors in both part a) and b) to the true result $f\left(1.53\right)=-7.60787$

asked 2021-12-15

How do you solve $9e+4=-5e+14+13e$

asked 2022-01-30

Is $f\left(x\right)=\frac{2}{{x}^{2}}-15x$ a polynomial?

asked 2022-01-21

Prove $\sum _{\{n=2\}}^{\mathrm{\infty}}\frac{1}{n\mathrm{ln}\left(n\right)\mathrm{ln}\mathrm{ln}n}$ is divergent.