# log expressions

• May 31st 2010, 07:28 PM
nuckers
log expressions
If log5=a and log36=b, determine an expression for log $\displaystyle 6/25$ in terms of a and b

I can get the log5 side, as 2a, but i can't seem to get the other side, is the expression wrong, or am i just confused, i can't seem to get 36log6,
• May 31st 2010, 07:34 PM
sa-ri-ga-ma
Quote:

Originally Posted by nuckers
If log5=a and log36=b, determine an expression for log $\displaystyle 6/25$ in terms of a and b

I can get the log5 side, as 2a, but i can't seem to get the other side, is the expression wrong, or am i just confused, i can't seem to get 36log6,

log36 = log(6)^2 = 2log(6) = b.

So log(6) = .....?
• May 31st 2010, 07:51 PM
nuckers
Quote:

Originally Posted by sa-ri-ga-ma
log36 = log(6)^2 = 2log(6) = b.

So log(6) = .....?

no, i dont understand it, i have to have 36log so b=36
• May 31st 2010, 07:58 PM
sa-ri-ga-ma
Quote:

Originally Posted by nuckers
no, i dont understand it, i have to have 36log so b=36

log(6) + log(6) = log(36) = b

So 2log(6) = b
Or log(6) = b/2
• May 31st 2010, 08:02 PM
undefined
log(6/25) = log(6) - log(25)

Using sa-ri-ga-ma's result, log(6) = b/2

Now for the other part,

a = log(5) = (1/2)(2 log(5)) = (1/2)log(25)

2a = log(25)

So combining, $\displaystyle \log\left(\frac{6}{25}\right) = \frac{b}{2}-2a$
• May 31st 2010, 08:21 PM
nuckers
thanks guys, but i'm just not seeing it, maybe i've just looked at too much math today, maybe a good nights sleep will make it better