Write the expression below as a single logarithm. Please show all of your work.
ln(xz^2)-3ln(x^3y)-1/2lnz

Write the expression below as a single logarithm. Please show all of your work.
ln(xz^2)-3ln(x^3y)-1/2lnz

@Mathematics

Question

Write the expression below as a single logarithm. Please show all of your work. 
ln(xz^2)-3ln(x^3y)-1/2lnz

@Mathematics

anonymous · Answer

ln(xz^2/ [(x^3y)^3*z^(1/2)])

anonymous · Answer

I came up with a different answer....mine was: 
loge(2^3/2/x^8y^3)
Is that the same?

anonymous · Answer

not it's not. when you combine logs, if you're subtracting it's division, addition is multiplication and any coefficients are exponents. so... alog(b)-clog(d) = log b^a/d^c

anonymous · Answer

ok so my answer is probably wrong then? I used a calculator, but must have entered it wrong. Is what you put the correct answer?

anonymous · Answer

you could simplify it to ln[ (z^(3/2)) / (x^5y^3) ]