Posted by **Tess** on Thursday, March 1, 2012 at 4:00am.

Expand using logarithm properties: log6 x(x+5)/x^6

I am so confused about this problem. Could anyone explain this to me?

- Math -
**Steve**, Thursday, March 1, 2012 at 11:56am
just as powers of products add (6^2 * 6^3 = 6^5) and subtract (6^8 / 6^3 = 6^5)

log of a product is the sum of the logs, and log of a quotient is difference of logs. That's because of the definition of log:

log_{6}N is the power of 6 needed to get N. Even though it looks weird, a log is just an exponent!

So, log x(x+5)/x^6

= logx + log(x+5) - log x^6

Now, log x^6 = log x*x*x*x*x*x = logx + logx + logx + logx + logx = 6logx

and now qwe end up with

logx + log(x+5) - 6logx

= log(x+5) - 5logx

That could also have been achieved by noticing that

x(x+5)/x^6 = (x+5)/x^5

notice how the power subtracted when factoring out the x?

## Answer This Question

## Related Questions

- Precalculus - Write 4log2+log6-log3 as a single logarithm. Explain with steps ...
- Math - Solve the equation. (the 6s are supposed to be sub-scripted, but I can't ...
- Math - The problem I have to solve is log with base 2 ^6 multiply by log base 6...
- precalulus - Ok feeling kinda dumb because this isn't coming out right. I know ...
- Algebra-Did I even begin correctly? - How would I write log(6)27-2log(6)3 as a ...
- ALGEBRA - CONTACT THE EXPRESSIONS.THAT IS USE THE PROPERTIES OF LOGARITHM TO ...
- math - give a problem that you could simlify using the communitive and ...
- Algebra 2 - Can someone please explain to me how to solve logarithmic equations...
- Logarithmic Algebra - let log2=a, log3=b, and log5=c. express the indicated ...
- Math - Which of the following is equal to log6(t + 1) − log6(t^2 − 1...

More Related Questions