Results 1 to 3 of 3

Thread: System of Equations, have to use exponent laws

  1. #1
    Junior Member
    Joined
    Sep 2016
    From
    Muskoka
    Posts
    58

    System of Equations, have to use exponent laws

    60^a=3 and 60^b=5. I have to find out the value of 12^((1-a-b)/(2-2b))? All i have figured out is 60^1-a-b=4 because 60^a+b=3*5=60/4, so 60^a+b-1=1/4, so 60^1-a-b=4. Don't know if it is relevant for this problem
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    2,076
    Thanks
    417

    Re: System of Equations, have to use exponent laws

    Quote Originally Posted by Ilikebugs View Post
    60^a=3 and 60^b=5.
    I have to find out the value of 12^((1-a-b)/(2-2b)).
    All i have figured out is 60^1-a-b=4 because 60^a+b=3*5=60/4,
    so 60^a+b-1=1/4, so 60^1-a-b=4.
    Can't tell what you're doing; you're showing sloppy stuff,
    like 60^1-a-b which should be 60^(1-a-b).

    Anyway:
    60^a = 3 ; so a = log(3) / log(60); similarly b = log(5) / log(60)

    Substitute results in 12^[(1-a-b)/(2-2b)] to get solution.
    Last edited by DenisB; Mar 22nd 2018 at 05:56 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2013
    From
    Lebanon
    Posts
    909
    Thanks
    435

    Re: System of Equations, have to use exponent laws

    $60=2^2 3^1 5^1$

    rewrite the two equations

    $2^{2a}3^{a-1}5^a=1$

    $2^{2b}3^b5^{b-1}=1$

    now eliminate $5$ (since the answer involves only the primes $2$ and $3$)

    ...

    $2^{2a}=3^{1-a-b}$

    next eliminate $3$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Exponent Laws
    Posted in the New Users Forum
    Replies: 11
    Last Post: Feb 2nd 2017, 06:34 PM
  2. Exponent laws!
    Posted in the Algebra Forum
    Replies: 5
    Last Post: Mar 11th 2014, 07:31 AM
  3. Exponent Laws
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Feb 20th 2013, 07:18 PM
  4. Exponent Equations (Laws of Indices)
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Jul 17th 2010, 10:32 AM
  5. Exponent Laws
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Sep 7th 2006, 07:09 PM

/mathhelpforum @mathhelpforum