Parker Bird

2022-07-22

How I could show that :$\mathrm{log}1=0$?

I would be like somone to show me or give me a prove for this :

Why $\mathrm{ln}1=0$?

Note that $\mathrm{ln}$ is logarithme népérien, the natural logarithm of a number is its logarithm to the base $e$.

Thanks for any replies or any comments!

I would be like somone to show me or give me a prove for this :

Why $\mathrm{ln}1=0$?

Note that $\mathrm{ln}$ is logarithme népérien, the natural logarithm of a number is its logarithm to the base $e$.

Thanks for any replies or any comments!

Lillianna Mendoza

Beginner2022-07-23Added 16 answers

$\begin{array}{rl}\mathrm{log}1=\mathrm{log}(1\cdot 1)& =\mathrm{log}1+\mathrm{log}1\\ \text{So}\mathrm{log}1& =\phantom{-}\mathrm{log}1+\mathrm{log}1\\ -\mathrm{log}1& \phantom{=}-\mathrm{log}1\\ 0& =\mathrm{log}1\end{array}$

Markus Petty

Beginner2022-07-24Added 2 answers

I will denote the natural logarithm of $x$ by $\mathrm{ln}x$

There are several definitions of the natural logarithm, so I will look at two of them.

1) $\mathrm{ln}(-):(0,\mathrm{\infty})\to \mathbb{R}$ is the inverse of the exponential function ${e}^{-}:\mathbb{R}\to (0,\mathrm{\infty})$, where $(0,\mathrm{\infty})$ denotes the set of positive real numbers. Then because ${a}^{0}=1$ for every real number $a$, particularly $e$, it follows that $\mathrm{ln}(1)=0$

2) $\mathrm{ln}x={\int}_{1}^{x}\frac{dt}{t}$. Then Evaluating at $1$ gives $\mathrm{ln}1={\int}_{1}^{1}\frac{dx}{x}=0$

There are several definitions of the natural logarithm, so I will look at two of them.

1) $\mathrm{ln}(-):(0,\mathrm{\infty})\to \mathbb{R}$ is the inverse of the exponential function ${e}^{-}:\mathbb{R}\to (0,\mathrm{\infty})$, where $(0,\mathrm{\infty})$ denotes the set of positive real numbers. Then because ${a}^{0}=1$ for every real number $a$, particularly $e$, it follows that $\mathrm{ln}(1)=0$

2) $\mathrm{ln}x={\int}_{1}^{x}\frac{dt}{t}$. Then Evaluating at $1$ gives $\mathrm{ln}1={\int}_{1}^{1}\frac{dx}{x}=0$

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

Which operation could we perform in order to find the number of milliseconds in a year??

$60\cdot 60\cdot 24\cdot 7\cdot 365$ $1000\cdot 60\cdot 60\cdot 24\cdot 365$ $24\cdot 60\cdot 100\cdot 7\cdot 52$ $1000\cdot 60\cdot 24\cdot 7\cdot 52?$ Tell about the meaning of Sxx and Sxy in simple linear regression,, especially the meaning of those formulas

Is the number 7356 divisible by 12? Also find the remainder.

A) No

B) 0

C) Yes

D) 6What is a positive integer?

Determine the value of k if the remainder is 3 given $({x}^{3}+k{x}^{2}+x+5)\xf7(x+2)$

Is $41$ a prime number?

What is the square root of $98$?

Is the sum of two prime numbers is always even?

149600000000 is equal to

A)$1.496\times {10}^{11}$

B)$1.496\times {10}^{10}$

C)$1.496\times {10}^{12}$

D)$1.496\times {10}^{8}$Find the value of$\mathrm{log}1$ to the base $3$ ?

What is the square root of 3 divided by 2 .

write $\sqrt[5]{{\left(7x\right)}^{4}}$ as an equivalent expression using a fractional exponent.

simplify $\sqrt{125n}$

What is the square root of $\frac{144}{169}$