Understanding Logarithms - Find log2, log2.0*10^24 and log5

[ayazabdul]

hello everybody,

please help me out, for i am not able to find out log2, log 2.0*10^24 , and log5.please explaine in detail...bye...thankyou..:shy:

 

[radou]

Don't you use a calculator?

 

[kesh]

hello everybody,

please help me out, for i am not able to find out log2, log 2.0*10^24 , and log5.please explaine in detail...bye...thankyou..:shy:

i'm guessing that this is a log base 10 question, and given log 2 relate it to the other two logs using the log rules for multiplication and division (5 being 10 divided by 2)

 

[ayazabdul]

ok, can please anyone explain how log 2.0*10^24 is equal to 24.30

 

[kesh]

ok, can please anyone explain how log 2.0*10^24 is equal to 24.30

i'm not going to do all the work, but

taking log 2 = 0.30 (all logs base 10)

use log [a*b]= log a + log b with a = 2 and b = 10^24

then use log[a^b] = b log a with a = 10 and b = 24

then log[10] = 1

 

[arunbg]

As Kesh mentioned, use log rules for multiplication and division, do you know these ?

 

[HallsofIvy]

First of all, no one can "explain how log 2.0*10^24 is equal to 24.30" because it isn't! That is an approximate value, correct to only two decimal places.

Do you know the "log rules" Kesh and arunbg referred to: log(ab)= log(a)+ log(b) and log(a^b)= b log(a) ? Apply those to log(2.0*10²⁴) to get, first,
log 2+ log 10²⁴. Then log 10²⁴= 24 log(10). The log(10) should follow from the definition of "log". log(2) you either look up in a table of common logarithms or use a calculator.