Thread: Rewriting Logs

I am a little confused on how to rewrite this

3lnx - 4lnx - 5lnt

it dosent seem right to right it as

$\displaystyle \ln \frac{\frac{ x^3}{x^4}}{ t^5}$

That actually is correct. Just simplify. $\displaystyle \frac{x^3}{x^4}=\frac{1}{x}$

So its just $\displaystyle \ln \frac{1}{xt^5}$

Or you could just combine like terms before attempting to rewrite it.
$\displaystyle 3\ln x-4\ln x=-\ln x$

Originally Posted by x5pyd3rx

I am a little confused on how to rewrite this

3lnx - 4lnx - 5lnt

it dosent seem right to right it as

$\displaystyle \ln \frac{\frac{ x^3}{x^4}}{ t^5}$

That's right but it's poor syntax

$\displaystyle \ln(x^3) - \ln(x^4) - \ln(t^5) = \ln \left(\frac{x^3}{x^4t^5}\right) = \ln \left(\frac{x^{-1}}{t^5}\right) = -\ln \left({xt^{5}}\right)$

Originally Posted by x5pyd3rx

I am a little confused on how to rewrite this

3lnx - 4lnx - 5lnt

it dosent seem right to right it as

$\displaystyle \ln \frac{\frac{ x^3}{x^4}}{ t^5}$

hi
$\displaystyle 3\ln x - 4\ln x - 5\ln t=(\ln x^3-\ln x^4)-\ln t^5=\ln(\frac{x^3}{x^4})-\ln t^5$

Originally Posted by x5pyd3rx

I am a little confused on how to rewrite this

3lnx - 4lnx - 5lnt

it dosent seem right to right it as

$\displaystyle \ln \frac{\frac{ x^3}{x^4}}{ t^5}$

$\displaystyle 3\ln{x} - (4\ln{x} + 5\ln{t})$

$\displaystyle \ln(x^3) - \ln(x^4 t^5)$

$\displaystyle \ln\left(\frac{x^3}{x^4 t^5}\right)$

$\displaystyle \ln\left(\frac{1}{x t^5}\right)$

$\displaystyle -\ln(x t^5)$

Crap i just got all this help and now i feel stupid because i wrote the problem wrong

its 3lnx - 4lny -5lnt

Originally Posted by x5pyd3rx

Crap i just got all this help and now i feel stupid because i wrote the problem wrong

its 3lnx - 4lny -5lnt

It's pretty much equal to skeeter's second step

$\displaystyle \ln \left(\frac{x^3}{y^4 t^5}\right)$