Question

Solve for n

4 = log(2^n -1)

Answer 1

\[4 = \log(2^n-1)\]

Answer 2

change it to exponential form
than it is a lot easier to solve

Answer 3

explain please?

Answer 4

ok logarithmic forms and exponential are interchange able i will show you

Answer 5

\[y=b^x, x=\log_b(y)\]

Answer 6

with the way you have your equation your b is equal to 10

Answer 7

so your equation will be...?

Answer 8

so I could say, n = -1 (4)

Answer 9

\[2^n-1=4^{10}\]

Answer 10

try to solve what I gave you

Answer 11

I forget logs, I'm not sure how to get the n out.

Answer 12

ok the formula can be reduced to \[2^n=1048575\]

Answer 13

log of 1048575 = 2 ?

Answer 14

oops sorry i mad one mistake is 104857

Answer 15

um not quite

Answer 16

log_2(n)=104857

Answer 17

\[\log_2(n)=104857\]
\[\frac{ \log(n) }{ \log(2) }=104857\]

Answer 18

multiply both sides by log(2)

Answer 19

are you still there?

Answer 20

yes

Answer 21

sorry, I'm trying to understand :-\

Answer 22

no problem it takes time

Answer 23

when there is a base of a number that is not ten you can split them like how i did

Answer 24

could you walk me through my problem?

\[80 = 20 \log (2^n - 1)\]

Answer 25

this only works for logs not lns and sure

Answer 26

divide both sides by 20

Answer 27

so first I divide by 20 and got what I said earlier..

\[4= \log(2^n - 1)\]

Answer 28

good now change to exponential i put up the formula. It took me a while to memorize that too so dont worry

Answer 29

now what is the base? 10?

Answer 30

yes

Answer 31

when a base is not written you automatically assume that it is 10

Answer 32

I can't simplify it more first?

Answer 33

2^n-1=4^10
should be the formula

Answer 34

no you have to change it to exponential

Answer 35

you can't simplify more because everything on the other side is in a log

Answer 36

so now I have to use log again, but this time base 2?

Answer 37

yes
but when that occurs you can use this formula where x is any number but 10
\[\log_b(y)=\frac{ \log(y) }{ \log(b) }\]

Answer 38

how are you so far

Answer 39

you should have gotten
\[\log(n)=\log(2)(4^{10}-1)\]

Answer 40

oops plus 1

Answer 41

\[\log(n)=315653.129763\]

Answer 42

now change back to exponential and you are done

Answer 43

um r you good?

Answer 44

sorry, minor emergency.

Answer 45

oh ok no problem

Answer 46

n = \[n= \frac{ \log(4+1) }{\log 2 }\]

Answer 47

I was doing something like that

Answer 48

but I think thats wrong too :-\

Answer 49

n = 10^315652.5277 ?

Answer 50

that can't be right...