Question

Simplify logarithms to rewrite the following expressions in terms of u and t. Let ln x=t and ln y = u.

[(ln x)^3 - ln (x^4)] / (lnx/e^2)ln(xe^2)


This problems is stumping me!!!! I don't know what to do, since some lnx are inside parentheses and others aren't.

Answer 1

well i don't know where is 'y' in the equation, but anyway the solution of this equation :

[(ln x)^3 - ln(x^4)] /[ln (x/e^2)ln(xe^2)] =
[(ln x)^3 - 4ln(x)] / [ ( ln(x) - ln(e^2)] [ ln(x) + ln(e^2) ] ; and now ln(x) =t;
t [ t^2 -4 ] / [( t -2ln(e)] [t + 2ln(e)] =
t[ (t - 2) (t +2 )] / [ ( t - 2 ) ( t + 2 ) ] = t = ln(x)

Answer 2

Thank you!!! This is great :) Yes, I didn't mean to add the Y there. Just meant to have t.

Answer 3

you are welcome :)