SOLUTION: Given that {{{log(10,(2))}}} is approximately 0.301 and {{{log(10,(3))}}} approx. 0.477, find {{{log(9,(8))}}}.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Given that {{{log(10,(2))}}} is approximately 0.301 and {{{log(10,(3))}}} approx. 0.477, find {{{log(9,(8))}}}.      Log On


   

Question 315465: Given that log%2810%2C%282%29%29 is approximately 0.301 and log%2810%2C%283%29%29 approx. 0.477, find log%289%2C%288%29%29.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Given that log%2810%2C%282%29%29 is approximately 0.301 and log%2810%2C%283%29%29 approx. 0.477, find log%289%2C%288%29%29.

Use the change of base formula:

log%28OLD_BASE%2C%28X%29%29=log%28NEW_BASE%2C%28X%29%29%2Flog%28NEW_BASE%2C%28OLD_BASE%29%29

Let the %22OLD_BASE%22 be 9 and the %22NEW_BASE%22 be 10, and X be 8.

Then we have:

log%289%2C%288%29%29=log%2810%2C%288%29%29%2Flog%2810%2C%289%29%29

Then write 

log%2810%2C%288%29%29 as log%2810%2C%282%5E3%29%29 

and

write log%2810%2C%289%29%29 as log%2810%2C%283%5E2%29%29

Then use the rule log%28B%2C%28A%5EC%29%29=C%2Alog%28B%2C%28A%29%29

to write those as

3log%2810%2C%282%29%29 

and

2log%2810%2C%283%29%29

So from start to finish we have:

 

Edwin