Question
how do you express in a single log and simplify
3/2 ln 4x^10 - 4/5 ln 2y^25
3/2 ln 4x^10 - 4/5 ln 2y^25
Answers
Damon
(3/2)ln 4 x^10 = (3/2)ln 4 + (30/2) ln x
but ln 4 = ln 2^2
so
3 ln 2 + 15 ln x
now the second term
- 4/5 ln 2y^25
-(4/5) ln 2 - 4 ln y
combining
(11/5) ln 2 + 15 ln x - 4 ln y
= ln [ 2*(11/5) x^15 /y^4 ]
check my arithmetic !
but ln 4 = ln 2^2
so
3 ln 2 + 15 ln x
now the second term
- 4/5 ln 2y^25
-(4/5) ln 2 - 4 ln y
combining
(11/5) ln 2 + 15 ln x - 4 ln y
= ln [ 2*(11/5) x^15 /y^4 ]
check my arithmetic !
oobleck
looks good, though I'd have written it
22x^15 / 5y^4
22x^15 / 5y^4