There are two properties of logs you should know; anything in front of a log can be put into the log as an exponent, and a sum/ difference of two logs can be written as a product or quotient of the things inside them, respectively.
So, ln(a+b)+ln(a-b) =ln((a+b)(a-b)), 3ln(c)=ln(c^3), and ln((a+b)(a-b)) (or if you prefer a^2-b^2)-ln(c^3)=ln((a^2-b^2)/(c^3). Hope that helps!
Answers & Comments
Verified answer
Rules of log
log of product = sum of logs
log (a*b) = log(a) + log(b)
log of division = difference of logs
log(a/b) = log(a) - log(b)
log of powers = multiplication of logs
log(a^7) = 7log(a)
These rules work both ways.
ln(a+b) + ln(a-b)
sum of logs, same as log of products
ln[(a+b)(a-b)] = ln(a^2 - b^2)
3ln(c) = multiplication of log = log of power
3ln(c) = ln(c^3)
- 3ln(c) = difference = division
Final answer
ln[ (a^2 - b^2) / c^3 ]
There are two properties of logs you should know; anything in front of a log can be put into the log as an exponent, and a sum/ difference of two logs can be written as a product or quotient of the things inside them, respectively.
So, ln(a+b)+ln(a-b) =ln((a+b)(a-b)), 3ln(c)=ln(c^3), and ln((a+b)(a-b)) (or if you prefer a^2-b^2)-ln(c^3)=ln((a^2-b^2)/(c^3). Hope that helps!
Ln {(a+b)(a-b)/c^3}
=Ln {(a^2-b^2)/c^3}
ln((a^2 - b^2)/c^3)