[MOVED] simple log Q: log[x^5/x-5] + log[3(x-5)/x] - 3logx

[april]

The question is: Write as a single log. Express any exponents as exponents rather than factors.

log[x^5/x-5] + log[3(x-5)/x] - 3logx

I started by...

log[(x^5/x-5)*3(x-5)/x] / 3logx

Not sure if that's right or what exactly what to do next.
I would appreciate the help. Thanks!

 

[o_O]

Not a bad start! (By the way, it's a subtraction sign before the 3logx, not a division sign).

So with something like this:

\(\displaystyle \L \log{\left(\frac{x^{5}}{x\,-\,5}\, \cdot\, \frac{3(x\,-\,5)}{x}\right)}\, -\, 3\log{(x)}\)

I would first simplify the inside of the first log expression so that it'll be easier to deal with later on. Cancel whatever you can cancel and see what you're left with.

After that, notice that 3logx can be represented without the coefficient. Recall the property:

log_ab^x = x log_ab

See how that applies? Tell us how you're doing after!

 

[april]

Thanks for the help. I'll work on it and let you know.