Results 1 to 4 of 4

Thread: Logarithm Problem URGENT!!!

  1. #1
    Newbie
    Joined
    Jan 2006
    Posts
    20

    Logarithm Problem URGENT!!!

    I have had a problem with logarithm problems and one in particular; the problem states: log 5^x+1= log 3^x. Can you please help me with this problem and explain the steps as well? Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by aussiekid90
    I have had a problem with logarithm problems and one in particular; the problem states: log 5^x+1= log 3^x. Can you please help me with this problem and explain the steps as well? Thank you.
    $\displaystyle \log 5^x+1=\log 3^x$, by the exponent rule for logarithms you may "bring down" the $\displaystyle x$ thus,
    $\displaystyle x\log 5+1=x\log 3$
    Then,
    $\displaystyle x\log 5-x\log 3=-1$
    Thus,
    $\displaystyle x(\log 5-\log 3)=-1$
    Thus,
    $\displaystyle x=-\frac{1}{\log 5-\log 3}=\frac{1}{\log 3-\log 5}$
    Q.E.D.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2006
    Posts
    20
    Sorry, typo, the problem would actually be 5^(x+1)=3^x
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by aussiekid90
    Sorry, typo, the problem would actually be 5^(x+1)=3^x
    Take the logarithm of both sides,
    $\displaystyle \log 5^{x+1}=\log 3^x$
    Now use the exponent rule and "bring down" exponents,
    $\displaystyle (x+1)\log 5=x\log 3$
    Open parantheses,
    $\displaystyle x\log 5+\log 5=x\log 3$
    Rearrange,
    $\displaystyle x\log 5-x\log 3=-\log 5$
    Factor,
    $\displaystyle x(\log 5-\log 3)=-\log 5$
    Thus,
    $\displaystyle x=-\frac{\log 5}{\log 5-\log 3}\approx -3.15$
    Q.E.D.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. logarithm problem
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Nov 28th 2011, 09:11 PM
  2. urgent help in logarithm
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: May 17th 2010, 03:26 AM
  3. Logarithm Problem
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: May 6th 2010, 08:22 AM
  4. Logarithm problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Feb 27th 2009, 12:12 AM
  5. Logarithm Urgent
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Oct 16th 2008, 12:31 AM

Search Tags


/mathhelpforum @mathhelpforum