DIfference Btw log base 10 and base 2? ..and how to comput base 2 on calculator?

Question

wats the diff, the textbook is confussing me with the two, becasue the teacher told us to use log base 2...and i used log base 10 ( direct imput into calculator - cos calculator is alwasy base 10 right?) and i STILL got the right answeer ...werid?

also can u use log base 2 on a calcualtor? or do u have to manually do change of base everytime?!?
THX!!! guys.

Answer 1

Hi,

To do log base 2 of 8, type in log (8)/log(2) into your calculator.

To do log base 23 of 481, type in log (481)/log(23) into your calculator.

Just type the log of your desired number divided by the log of the base. Be sure to close parentheses around each number to get correct answers.

I hope that helps!! :-)

Answer 2

Base 2 Table

Answer 3

Let log represent log base 10, log 15 = log (3*10/2) = log 3 + log 10 - log 2 = 1.176

Answer 4

The way to think of logarithms is if I have a number like 5 and I raise it to some unknown power and get 37, what power did I raise it to? Back in the day they made tables so they could solve that quickly.They also realized they could easily convert things to base 10, so they would then only need one table. Lets say you have 2 to the x power equals 7. To solve that you can write it in logarith form, which is log base 2 of 7 equals x. Or you can take the log base 10 of both sides of the original equation (2 to the x power equals 7). Taking the log base 10 of both sides yields log base 10 of 2 to the x equals log base 10 of 7. I can use one of the logarithm rules to move the x out in front, so I get x times log base 10 of 2 equals log base 10 of 7. Dividing both sides by log base 10 of 2 yields the equation x equals log base 10 of 7 divided by log base 10 of 2. You can put that in your calculator. Note I started with 2 to the x power equals 7, but before that I told you how to get to that point from the point your original problem asked as the starting point.

Answer 5

Fist of all, how can it be the same?

Log base 2 of 8 is Log base 2 of 2^3 = 3 Log base 2 of 2 = 3
Log base 10 of 8 is 0.903 (using the calc)

Here is the formula for changing base

log base a of x = log base b of x /log base b of a
hence the answer in the others

Answer 6

nearly all caculater are set for log base 10 as this is the commonly used one there is a formular for the changein of bases

logb X = logk X / logk b

k bin the new base (in ur case 2).

An easier way of thinking about logs is using
10^2 =100 or rearanged log 100 = 2 (the base of this log being 10)

therefore (a,b bin any random value given)
2^a= b or rearanged log b = c ( the base of this log being 2)

the general formular being (a,b,c being constants)

a^b = c therefore log(a) b = c

that should help explain the difference but to be honest log are dam hard but once u get ur head round it all question are easy enough to do.

Answer 7

lets say you have a problem of 3 Log base 2
just pus 3 log, then divide it by 2 log

if that doesn't work, swap them! I can't remember the order.

then you have the answer!

Answer 8

If log (base x) of y=z
then that means x^z=y.

For calculators:
log (base x) of y=
(log (base 10) of y)/(log (base 10) of x).

Answer 9

Base 2 system is completely made up of 0 and 1
base 10 is made of 1,2,3,4,5,6,7,8,9

1 =1
10=2
11=3
100=4
101=5
110=6
111=7
1000=8