Results 1 to 3 of 3

Math Help - PROVE LOG PROPERTY!

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    2

    PROVE LOG PROPERTY!

    i have a advance algebra question is about LOG.!
    Can someone help me with these questions?

    I need to prove each property by using the format like this:
    Change of Base
    Let y=LOGa X
    1.then a to the power of y=x definition of logarithm.
    2.LOGb a to the power of y=LOGb X take LOGb of both sides
    3.y times LOGb a=LOGb X log of a power
    4.y= LOGb X / LOGb a, QED divide by LOGb a

    CAN SOMEONE HELP ME WITH THE FOLLWOING QES?

    Direct Proportionality
    LOGa=(c)(LOGb X),where c is a constant.

    Product of two logs
    (LOGa B)(LOGb C)=LOGa C

    log with a power for its base
    LOG(b to the power n) X=1/n LOGb X

    base and argument are reciprocals
    LOG1/b 1/X =LOGb X

    I NEED IT FOR TOMORROW!!
    THANK YOU SO MUCH!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,811
    Thanks
    116
    Quote Originally Posted by kellyliu View Post
    i have a advance algebra question is about LOG.!
    Can someone help me with these questions?

    I need to prove each property by using the format like this:
    Change of Base
    Let y=LOGa X
    1.then a to the power of y=x definition of logarithm.
    2.LOGb a to the power of y=LOGb X take LOGb of both sides
    3.y times LOGb a=LOGb X log of a power
    4.y= LOGb X / LOGb a, QED divide by LOGb a

    CAN SOMEONE HELP ME WITH THE FOLLWOING QES?

    Direct Proportionality
    LOGa=(c)(LOGb X),where c is a constant.

    A) Product of two logs
    (LOGa B)(LOGb C)=LOGa C

    B) log with a power for its base
    LOG(b to the power n) X=1/n LOGb X

    C) base and argument are reciprocals
    LOG1/b 1/X =LOGb X

    I NEED IT FOR TOMORROW!!
    THANK YOU SO MUCH!!
    To A):
    Obviously B = b

    \log_a(b) \cdot \log_b(c)=\dfrac{\log(b)}{\log(a)} \cdot \dfrac{\log(c)}{\log(b)}=\dfrac{\log(c)}{\log(a)}=  \log_a(c)

    to B):

    \log_{b^n}(X)=\dfrac{\log(X)}{\log(b^n)}=\dfrac{\l  og(X)}{n \log(b)}=\dfrac1n \cdot \dfrac{\log(X)}{\log(b)}=\dfrac1n \cdot \log_b(X)

    to C):

    \log_{\frac1b}\left(\dfrac1x\right)=\dfrac{\log\le  ft(\dfrac1x\right)}{\log\left(\dfrac1b\right)} = \dfrac{-\log(x)}{-\log(b)}=\dfrac{\log(x)}{\log(b)}=\log_b(x)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2008
    Posts
    2
    thank you sooo much!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove a property about a bit string
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 29th 2011, 11:07 PM
  2. [SOLVED] Prove by Archimedian property
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 28th 2011, 07:44 PM
  3. Replies: 1
    Last Post: February 20th 2011, 04:11 PM
  4. Replies: 6
    Last Post: July 11th 2010, 08:11 AM
  5. prove inequality property
    Posted in the Algebra Forum
    Replies: 4
    Last Post: September 8th 2008, 07:07 PM

Search Tags


/mathhelpforum @mathhelpforum