Results 1 to 3 of 3

Math Help - Logs???

  1. #1
    daniella
    Guest

    Exclamation Logs???

    how do i use the "change of base" formula to solve

    1 a) 3^2x=8
    it is the exponent 2x
    2 d) 5^x-2=150
    it is to the exponent x-2

    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
    9
    Quote Originally Posted by daniella View Post
    how do i use the "change of base" formula to solve

    1 a) 3^2x=8
    it is the exponent 2x
    3^{2x}=8=2^3
    Thus,
    2x=3
    x=1.5
    2 d) 5^x-2=150
    it is to the exponent x-2
    5^{x-2}=150
    Thus,
    \log_5 150=x-2
    x=2+\log_5 150
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,658
    Thanks
    598
    Hello, daniella!

    You're expected to know that b^x\:=\:a is equivalent to x \:=\:\log_ba
    . . and the Base-change formula: . \log_aX \;=\;\frac{\log_bX}{\log_ba}


    How do i use the "change of base" formula to solve:

    1\:a)\;3^{2x}\:=\:8

    2\:d)\;5^{x-2}\:=\:150

    "Change of Base" formula: . \log_aX \:=\:\frac{\log_bX}{\log_ba}


    1a) We have: . 3^{2x} \:=\:8 . . . which is equivalent to: . 2x \:=\:\log_38

    Change-of-base: . 2x\:=\:\frac{\log8}{\log3}

    Therefore: . x \;=\;\frac{\log8}{2\cdot\log3} \;\approx\;0.9464


    2d) We have: . 5^{x-2}\;=\;150 . . . which is equivalent to: . x-2 \;=\;\log_5150

    Change-of-base: . x-2\;=\;\frac{\log150}{\log5}

    Therefore: . x \;=\;\frac{\log150}{\log5} + 2 \;\approx\;5.1133

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 9
    Last Post: February 22nd 2011, 05:39 PM
  2. Logs
    Posted in the Algebra Forum
    Replies: 4
    Last Post: April 24th 2010, 07:52 AM
  3. Logs
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 10th 2009, 06:08 PM
  4. Dealing with Logs and Natural Logs
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: April 14th 2008, 06:18 AM
  5. several questions-logs/natural logs
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 12th 2007, 08:58 PM

/mathhelpforum @mathhelpforum