SOLUTION: Are the following statement true or false? 1)log(a,(b^4)) =(log(a,(^b)))^4 2)ln5sqrt(xy)=-5(lnx+lny) 3)lne^3=ln^5-lne^2 4)ln((3^b)(a^b))=b(lna+ln3) I have answered these a

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Are the following statement true or false? 1)log(a,(b^4)) =(log(a,(^b)))^4 2)ln5sqrt(xy)=-5(lnx+lny) 3)lne^3=ln^5-lne^2 4)ln((3^b)(a^b))=b(lna+ln3) I have answered these a      Log On


   

Question 998835: Are the following statement true or false?
1)log(a,(b^4)) =(log(a,(^b)))^4
2)ln5sqrt(xy)=-5(lnx+lny)
3)lne^3=ln^5-lne^2
4)ln((3^b)(a^b))=b(lna+ln3)
I have answered these and one of them are wrong, I am not sure which one I got wrong.
1)False
2)True
3)False
4)False
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1)
log%28a%2C%28b%5E4%29%29+=%28log%28a%2C%28b%29%29%29%5E4
4log%28a%2C%28b%29%29+%3C%3E%28log%28a%2C%28b%29%29%29%5E4
answer: false
2)
ln%285sqrt%28xy%29%29=-5%28ln%28x%29%2Bln%28y%29%29
ln%285%28xy%29%5E%281%2F2%29%29=-5%28ln%28x%2Ay%29%29
%281%2F2%29ln%28%285x%29%285y%29%29=-5%28ln%28x%2Ay%29%29
%281%2F2%29%28ln%285x%29%2Bln%285y%29%29%3C%3E-5%28ln%28x%2Ay%29%29
answer: false
3)
ln%28e%5E3%29=ln%28e%5E5%29-ln%28e%5E2%29+
ln%28e%5E3%29=ln%28e%5E5%2Fe%5E2%29+
ln%28e%5E3%29=ln%28e%5E3%29+
answer: true
4)
ln%28%283%5Eb%29%28a%5Eb%29%29=b%28ln%28a%29%2Bln%283%29%29
ln%28%283%5Eb%29%28a%5Eb%29%29=b%28ln%283a%29%29
ln%28%283%5Eb%29%28a%5Eb%29%29=ln%28%283a%29%5Eb%29%29
ln%28%283%5Eb%29%28a%5Eb%29%29=ln%28%283%5Eb%29%28a%5Eb%29%29
answer: true