Applying Logarithmic Functions to Password Entropy and Star Brightness

this video is about application of logarithm functions password entropy is a matter of predictability of a computer

password the higher the entropy the more difficult it is to guess the password the relationship between the password

and p p measured in bits and the number of gesses G required to decode the password is given by this

function calculate the value of P for a password that takes 5,000 guesses to decode 5,000 guesses let's go back to

this uh function G is number of gases p

is the relationship between the password entropy so this 5,000 guesses is G then we do the

substitution for this equation 0.46 P equals log base 10 of 5,000 by

solver control menu clear the history let's type the equation first log you will do control 10 to the X

power base is 10 of 5, then control menu enter enter enter

M series 9.1 at a 36 fix P equal 9.11 B write down G as a function of for

p in other words you need to change this uh log into exponential function we do know the inverse function of for

logarithm function is the exponential function so what we have log base 10 of x = c we

will put a base 10 both sides then we can cancel we got x = 10 to the 6

power another logarithm function we will use a lot is a natural

log natural log of x = d we do know natural log of x equals log

base e of X so we will add e as base both sides x = e to the this power for this

function 0.4 6 P = log base 10 of G we will

add 10 as the base both sides then cancel we got g equals 10 to the

0.406 P power this is the function we are looking for four let's go to say find the number of gases required to

decode a password that has an entropy of 28 bits which means the p = 28 write your answer in the form of

this since uh we already got the function for G we will just uh plug in p = 28 into this

function so we got G = 10 to the 0.46 time 28 power equals 10 to the

0.46 times the 28 enter

2.33 * 10 to the 11 power if you are not sure this equation is right or wrong you

can directly use this function we will substitute p = 28 into this original function we got

0.46 * 28 equals common log base 10 of

G first of all we need to type in the equation control 10 to the X power to get log base 10 of G

control menu enter enter enter you could have see domain error in

this case you need to put value for lower Bond and a upper Bond go up

enter delete extra stuff only leave the equation control

menu lower we will put in zero upper let's do 10 to the 100 power just put the big number here then enter enter

we got the solution 2.33 * 10 to the 11 Power by solver G = 2.33 * 10 to the 11 power let's go to

last one there is a point on the graph of a function G of p with the coordinates Z one so P equal zero and

gals 1 explain what this coordinate values mean in the context of the computer

passwords p is password entropy D is the number of guesses to decode the password when you answer this

question you have to write down the entropy is zero and a number of guesses is one to decode the password

when entropy of the password is zero only one guess can decode the password which means your password is very weaks

are classified by their brightness the brightest stars in the sky have a magnitude of one the magnitude M of

another star can be modeled as a function of its brightness B relative to a star of magnitude one as shown by the

following equations the star called acub has a brightness of

0.525 find the magnitude of acant we know b means the brightness m is the

magnitude we are given brightness 0.05 to 5 which means b equal 0.05

to5 so you need to do the substitution m = 1 -

2.5 log base 10 of 0.525 go to calculator 4.20 as a 36 f

or you can write down the whole thing put the dot dot dot as a full answer m equals

4.2 Series has a magnitude of 4 S and is the least bright star visible without magnification find the brightness of

series magnitude of seven means this m equals 7 so we will substitute M = 7 into this

function we will get 7 = 1 - 2.5 log base 10 of for B let's go to solver control menu clear the history

seven = 1 - 2.5 * control 10 to the X power let's go to

log base 10 of b control menu enter enter enter we won't get this

uh answer this said domain error for the log we know this B must be positive number let's retype for this equation

control menu enter enter make sure for log equation for lower Bond you always put the zero

for upper Bond you can put the 10 to the 100 power enter we got the solution b equals

0. 3981 dot dot dot or 0.398 let's go to see find how many

times brighter acant is compared to series how many

times means we need to do the division the brightness of acant is given 0.05

to five the brightness of series is here 0.398 control divide

0.525 over try to put accurate answer we will do 0.3 981

from previous calculation enter

13.2 as a 3 Sig fix answer is 13.2