For these properties we will suppose that x > 0 and y > 0

log_b ( xy ) = log_b x + log_b  y

log_b (    x/y) = log_b  x - log_b  y

log_b (x^r ) = r log  x

If log_b x = log_b  y then x = y .

 We won't be doing anything along the final property in this section; this is here only for the sake of completeness. We will be looking at this property thoroughly in a couple of sections.

The first two properties illustrated here can be a little confusing primary since on one side we've got a product or quotient within the logarithm & on the other side we've got a sum or disparity of two logarithms.  We will only have to be careful with these properties & ensure to them correctly.

Also, note that there are no rules on how to break up the logarithm of the sum or difference of two terms.  To be apparent about this let's note the following,

logb ( x + y ) ≠ logb  x + logb  y

logb ( x - y ) ≠ logb  x - logb  y

Be careful along with these and do not attempt to use these as simply they aren't true.

Note that every property given to this point is valid for the common and natural both logarithms.  We only didn't write them out explicitly by using the notation for these 2 logarithms, the properties do hold for them nonetheless

Posted Date: 4/8/2013 3:22:03 AM | Location : United States

Ask an Expert

Related Discussions:- Manipulation properties of the logarithm, Assignment Help, Ask Question on Manipulation properties of the logarithm, Get Answer, Expert's Help, Manipulation properties of the logarithm Discussions

Write discussion on Manipulation properties of the logarithm
Your posts are moderated

Write your message here..

Related Questions

Scientific notation, (9x10^1)(2.3x10^0) (9x10^1)(2.3x10^0)

Percentage, #quewhat is the origal value if a shirt cost $15 before the sal... #quewhat is the origal value if a shirt cost $15 before the sale and cost $12 in the sale.

Radical expressions, (x2/3)-3 (x2/3)-3

How to do algebra 1, how do you do algebra 1? how do you do algebra 1?

Olve, Find the number of permutations of them word helicopter Find the number of permutations of them word helicopter

Natural log, e^4x-5 -8=14403 Solution in Natural Log e^4x-5 -8=14403 Solution in Natural Log

How can you help me, can you help me in algebra can you help me in algebra

Using square roots, x2=4 x2=4

Solving multi step ecuation equations, what is the answer for this 2n+3... what is the answer for this 2n+3n+7=-41

CBA, I am preparing for a CBA what do I need to study? I am preparing for a CBA what do I need to study?