Recent questions in Logarithmic Functions

Logarithmic Functions
Answered

Bierlehre59
2022-08-14

i.e. suppose f is a function and n is a real number, is $\mathrm{log}(f(x{)}^{n})=n\xb7\mathrm{log}(f(x))$?

Logarithmic Functions
Answered

sondestiny120g
2022-08-11

${e}^{x}=\sum _{n=0}^{\mathrm{\infty}}\frac{{x}^{n}}{n!}$

$\mathrm{log}(x)=\sum _{n=1}^{\mathrm{\infty}}\frac{(-1{)}^{n+1}(x-1{)}^{n}}{n}$

Where second series converges when |x−1|<1.It is possible to prove that:

${e}^{\mathrm{log}(x)}=x$

for $|x-1|<1$ using only series representation?

Logarithmic Functions
Answered

logosdepmpe
2022-08-11

${\mathrm{log}}_{3}(\frac{x({x}^{2}+5)}{\sqrt{{x}^{2}-5}})$

Logarithmic Functions
Answered

Garrett Sheppard
2022-08-10

$f(x)=\mathrm{ln}({e}^{x}+3)$

Because the argument of $f,\phantom{\rule{thinmathspace}{0ex}}{e}^{x}+3,$, is a nonnegative number, ${e}^{x}+3>0$ and ${e}^{x}>-3.$ Taking natural logarithms on both sides, we get $x>\mathrm{ln}(-3)$. However, the domain of a logarithmic function must be nonnegative real numbers, so $\mathrm{ln}(-3)$ doesn't make sense. How then to determine the scope of the original function?

Logarithmic Functions
Answered

granuliet1u
2022-08-10

$\mathrm{ln}(x)+\mathrm{ln}(x-1)=1$

I take ex of both sides:

$x+x-1=e$

$2x\u20131=e$

$2x=e+1$

$x=\frac{e+1}{2}$

Logarithmic Functions
Answered

Ledexadvanips
2022-08-06

Logarithmic Functions
Answered

Braylon Lester
2022-07-22

With the same way of thinking is ${\mathrm{log}}_{2}(x)+x$ a logarithmic?

Logarithmic Functions
Answered

scherezade29pc
2022-07-21

$\int \frac{{\mathrm{ln}}^{3}x}{x}\text{}dx$

Is this the same as

$\int \frac{(\mathrm{ln}x{)}^{3}}{x}\text{}dx\phantom{\rule{thickmathspace}{0ex}}\phantom{\rule{thickmathspace}{0ex}}?$

Logarithmic Functions
Answered

Patricia Bean
2022-07-20

What is the range of $\{-{b}^{2}\mathrm{log}(b)\}$? Does it range $(-\mathrm{\infty},+\mathrm{\infty})$?

How can I show $\frac{-b\mathrm{log}(b)}{1-b}\le 1$ ?

Logarithmic Functions
Answered

Emmanuel Pace
2022-07-20

The answer to this is:

$\frac{dy}{dx}=(3{x}^{2}+2{)}^{lnx}(\frac{1}{x}ln(3{x}^{2}+2)+\frac{6xlnx}{3{x}^{2}+2})$

What I'm coming up with is:

$\frac{dy}{dx}=(3{x}^{2}+2{)}^{lnx}(\frac{1}{x}ln(3{x}^{2}+2)+\frac{6x}{3{x}^{2}+2})$

What I'm not understanding is where the $\frac{6xlnx}{3{x}^{2}+2}$ comes from, if anyone could explain this I'd really appreciate it.

Logarithmic Functions
Answered

Rishi Hale
2022-07-18

Logarithmic Functions
Answered

Nash Frank
2022-07-17

$\frac{1}{3}\mathrm{ln}(x+2{)}^{3}+\frac{1}{2}[\mathrm{ln}(x)-\mathrm{ln}({x}^{2}+3x+2{)}^{2}]$

b) Solve each equation for x.

1)${e}^{5-4x}=4$

x=?

2) $\mathrm{ln}(3x-13)=8$

x=?

Logarithmic Functions
Answered

Patricia Bean
2022-07-17

$f\left(x\right)=\sqrt{\mathrm{log}\left(\frac{3x-{x}^{2}}{2}\right)}$

Logarithmic Functions
Answered

pliwraih
2022-07-16

$f(n)={n}^{0.999999}\mathrm{log}n=O({n}^{0.999999}{n}^{0.000001})$?