0
$\begingroup$

Express as a single logarithm with a coefficient of 1:

$$ 2(\ln(x)-\ln(x+1))-3(\ln(x^2)-\ln(x^2-1)) $$ I've been trying for nearly an hour and can't seem to find the answer, can anyone help plz :S

$\endgroup$
3
$\begingroup$

Looks like this what you are looking for: [first note that $\ln a+\ln b=\ln(ab)$, $\ln a-\ln b=\ln(a/b)$ and $x\ln a=\ln (a^x)$; assuming all the $\ln$'s exist]

Your expression $$=2\ln x+3\ln(x^2-1)-[2\ln(x+1)+3\ln(x^2)]$$ $$=\ln[x^2.(x^2-1)^3]-\ln[(x+1)^2.(x^2)^3]$$ $$=\ln\frac{x^2.(x^2-1)^3}{(x+1)^2.x^6}$$ $$=\ln (1+\frac{1}{x})(1-\frac{1}{x})^3$$

$\endgroup$
0
$\begingroup$

Use the following rules for logarithms:

$$\ln(a)-\ln(b) = \ln\left(\frac{a}{b}\right)\\ c\cdot \ln(d) = \ln(d^c)$$

$\endgroup$
  • $\begingroup$ Did you mean $c\ln(d)=\ln(d^c)$? $\endgroup$ – E.O. Sep 19 '12 at 4:22
  • $\begingroup$ @E.O. Whoops. Yes. I've edited to fix the error. $\endgroup$ – Richard Sullivan Sep 19 '12 at 12:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.