Group 3: Suzanne, Christian, Mark
We found out that this equation is true, here is our solution...
One of the laws of logarithms is: log(M/N)=logM-logN, also known as the Quotient law .
Using the Quotient law, ln(A/B)=lnA+ln(1/B), the blue part can be simplified to ln(A/B)=lnA+ln1-lnB.
If you solve for ln1, it equals 0. So our equation, ln(A/B)=lnA+ln1-lnB
simplifies to ln(A/B)=lnA+0-lnB
ln(A/B)=lnA-lnB The equation holds true, if you go back to our Quotient law (log(M/N)=logM-logN).
ln(A/B)=lnA-lnB can be simplifed to ln(A/B)=ln(A/B)
ln(A/B)=lnA-lnB can be simplified to lnA-lnB=LnA-ln B
Here is a possible mistake a person might make when writing this equation as:
Instead of using the quotient law correctly, someone may subtract ln(1/B). IF they subtract like this, they have made their first mistake.>>>ln(A/B)=lnA-(ln1-lnB)
The right side of the equation results in an addition, WHICH IS DIFFERENT FROM THE QUOTIENT LAW. ln(A/B)=lnA+lnB
The above equation would simplify to this:
ln(A/B)=ln(AB) SEE THE DIFFERENCE?on the left side the values are being divided. On the right side, the values are multiplied
The reason someone might do this is by mistakenly applying the logarithmic law log(M/N)=logM-logN to this question twice.