Question

Log1/100

Answer 1

\(\bf log\left(\frac{1}{100}\right)?\)

Answer 2

yes sir

Answer 3

I have a rule but i dont know if it applies to it.

Answer 4

I have to simplify it without a calculator as well.

Answer 5

http://www.chilimath.com/algebra/advanced/log/images/rules%20of%20exponents.gif <--- rule 2 listed there applies

Answer 6

so would it be Log 1- Log 100?

Answer 7

recall that when the log base is skipped, is implicitly taken as base 10 so \(\bf log\left(\frac{1}{100}\right)\implies log_{10}\left(\frac{1}{100}\right)\)

Answer 8

yeap

Answer 9

ahh so then would i put it in exponent form would it be 10^.001?=1/100

Answer 10

I'm not sure if the .001 is correct but I'd like some help on this

Answer 11

\(\bf log\left(\frac{1}{100}\right)\implies log_{10}\left(\frac{1}{100}\right)\implies log_{10}1-log_{10}100
\\ \quad \\
log_{\color{red}{ a}}{\color{blue}{ b}}=y\implies {\color{red}{ a}}^y={\color{blue}{ b}}\qquad thus
\\ \quad \\
log_{{\color{red}{ 10}}}{\color{blue}{ 1}}-log_{{\color{red}{ 10}}}{\color{blue}{ 100}}\implies ?\)

Answer 12

uh.. Log10 99?

Answer 13

log10 -99*

Answer 14

\(\large {log_{{\color{red}{ 10}}}{\color{blue}{ 1}}-log_{{\color{red}{ 10}}}{\color{blue}{ 100}}\implies
\begin{cases}
{\color{red}{ 10}}^\square =1&\to \square =?\\
{\color{red}{ 10}}^\square =100&\to \square =?
\end{cases} }\)

Answer 15

OHHH its 1/10?

Answer 16

no wait...

Answer 17

well.... what are the two \(\square\) though ?

Answer 18

the one for the bottom is 10^10=100

Answer 19

im figuring out the top one.

Answer 20

ok

Answer 21

0?

Answer 22

\(\bf 10^10\ne 100\)

Answer 23

wait was it 0?

Answer 24

woops anyhow \(10^{10}=100\)

Answer 25

wait a second shoot yes \(\large log_{{\color{red}{ 10}}}{\color{blue}{ 1}}-log_{{\color{red}{ 10}}}{\color{blue}{ 100}}\implies
\begin{cases}
{\color{red}{ 10}}^0 =1\to \square =0\\
{\color{red}{ 10}}^\square =100\to \square =?
\end{cases}\)

however \(\large 10^{10}\ne 100\)

Answer 26

\(\bf 10^{10} = 10000000000\)

Answer 27

oh wow im thinking multiplication... I keep forgetting its 2...

Answer 28

yeap \(\large {
log_{{\color{red}{ 10}}}{\color{blue}{ 1}}-log_{{\color{red}{ 10}}}{\color{blue}{ 100}}\implies
\begin{cases}
{\color{red}{ 10}}^0 =1\to \square =0\\
{\color{red}{ 10}}^2 =100\to \square =2
\end{cases}
\\ \quad \\
thus \qquad log(1)-log(100)\implies 0-2 }\)

Answer 29

so -2

Answer 30

yeap

Answer 31

wooow makes sense thanks so much I appreciate it very much.

Answer 32

yw