SOLUTION: Given log2on the base 10 =.3010, find log200on the base25 by using log table

Question 970606: Given log2on the base 10 =.3010, find log200on the base25 by using log table
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
not exactly sure what you mean by this, but one way to solve this is as follows:

in the following:

big L means log and L(x) means log of x to the base of 10 and L25(x) means log of x to the base of 25.

using that convention:

log(2) on the base of 10 is represented as L(2).

log(200) on the base of 25 is represented as L25(200) which can be converted to base of 10 to make it equal to L(200)/L25).

so you get L(2) = .3010 and you want to find the value of L(200)/L(25)

L(200)/L(25) can be expressed as L(2*100)/L(100/4).

this can be expressed as (L(2) + L(100)) / (L(100 - L(4)).

this can be expressed as (L(2) + L(10^2)) / (L10^2) - L(2^2)).

this can be expressed as (L(2) + 2*L(10)) / (2*L(10) - 2*L(2))

you are given that L(2) = .3010.
actually L(2) is equal to .3010299957.

using the unrounded number makes confirming your solution easier down the road, so i'll use that instead of .3010.

since L(10) is equal to y if and only if 10^y = 10 if and only y = 1, then you get:

L(10) = 1.

your expression of (L(2) + 2*L(10)) / (2*L(10) - 2*L(2)) becomes:

(.3010299957 + 2*1) / (2*1 - 2*.3010299957) which becomes:

(.3010299957 + 2) / (2 - 2*.3010299957) which becomes:

2.3010299957 / 1.397940009 which becomes 1.646014837

you can confirm this is true by using your calculator to get L(200)/L(25) = 1.646014837

since they're the same, the solution is good.

RELATED QUESTIONS
given log 7=0.8451 and log 2 =0.3010, find the value of log 28. (answered by Alan3354,Theo,ikleyn,MathTherapy)

Given that log(2) ≈ 0.3010, find the value of the logarithm.... (answered by ikleyn)

How to find log (5,512) ? i.e., log 512 to the base 5.. log 2 base 10 =0.3010 and log 3... (answered by jsmallt9)

Find the value of 0.8176*13.64 by using log... (answered by lynnlo)

instead of using table what is the constant or formula to find log of any number with... (answered by rfer,Alan3354)

Given log 2=.3010 and log 3=.4771, evaluate log 6 Can you multiply the logs to get the... (answered by MathTherapy)

Using a calculator, find log 1000 where log means log to the base of... (answered by stanbon)

Using a calculator, find log 10000 where log means log to the base of... (answered by bucky)

Given Log 2=.3010 and log 3 =.4771, find: a. log (240) b. log... (answered by jsmallt9)