Question

ln(√(6m^4n^2)) write as a sum and/or difference of logarithms, with all variables to the first degree... I know the answer is 1/2ln(6) + 2ln(m) + ln(n) but I don't understand where 1/2 half comes from??

Answer 1

It's the square root.\[\ln(\sqrt{6m^4n^2})=\ln(6m^4n^2)^{\frac{1}{2}}=\frac{1}{2}\ln(6m^4n^2)=...\]

Answer 2

The rule \[lna^b=b \cdot \ln a\] has been used

Answer 3

is the 1/2 used to get rid of the √ (square root)?

Answer 4

√a=a^(1/2), because:\[(\sqrt{a})^2=a\]and\[(a^{\frac{1}{2}})^2=a^{2 \cdot\frac{1}{2}}=a^1=a\]
It is just another way of writing √a.

Answer 5

Oooh. I remember that now. Wow you have been a HUGE help. Thank you so much

Answer 6

yw!