SOLUTION: 2 log(base 4) 9 - log(base 2) 3

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Question 206454: 2 log(base 4) 9 - log(base 2) 3
Found 3 solutions by stanbon, MathTherapy, greenestamps:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2 log(base 4) 9 - log(base 2) 3
---
= 2[log9/log4] - [log3/log2]
-------
= 3.1699 - 1.585
= 1.585
=================
Cheers,
Stan H.

Answer by MathTherapy(10699) About Me  (Show Source):
You can put this solution on YOUR website!
2 log(base 4) 9 - log(base 2) 3

highlight%282%2Alog+%284%2C+%289%29%29+-+log+%282%2C+%283%29%29%29
2%2A%28log+%282%2C+%289%29%29%2Flog+%282%2C+%284%29%29%29+-+log+%282%2C+%283%29%29
2%2A%28log+%282%2C+%289%29%29%2F2%29+-+log+%282%2C+%283%29%29
cross%282%29%2A%28log+%282%2C+%289%29%29%2Fcross%282%29%29+-+log+%282%2C+%283%29%29
log+%282%2C+%289%29%29+-+log+%282%2C+%283%29%29
log+%282%2C+%289%2F3%29%29 = highlight%28log+%282%2C+%283%29%29%29

I think this is what you want: the above log expression to be SIMPLIFIED into a SINGLE log, and not calculated as the other person did!

Answer by greenestamps(13292) About Me  (Show Source):
You can put this solution on YOUR website!


Here is another path to simplifying this expression using the following property of logarithms:

log%28b%2C%28a%29%29=log%28b%5En%2C%28a%5En%29%29

In this problem, 4=2%5E2 and 9=3%5E2, so log%284%2C%289%29%29=log%282%2C%283%29%29

Then we have



ANSWER: log%282%2C%283%29%29