1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solving Exponential Equations

  1. Jan 26, 2012 #1
    1. The problem statement, all variables and given/known data
    Solve [itex]2^{k-2}=3^{k+1}[/itex]



    2. Relevant equations



    3. The attempt at a solution
    [tex]2^{k-2}=3^{k+1}[/tex]
    [tex]\frac{2^{k}}{2^{2}}=(3^k)(3^1)[/tex]
    [tex]\frac{2^{k}}{3^{k}} = 4 \cdot 3[/tex]
    [tex]\frac{2^{k}}{3^{k}} = 12[/tex]

    What do I do next to solve for K?
     
  2. jcsd
  3. Jan 26, 2012 #2

    Mentallic

    User Avatar
    Homework Helper

    Use the fact that [tex]\frac{a^n}{b^n}=\left(\frac{a}{b}\right)^n[/tex] and also, what do you know about logarithms?
     
  4. Jan 27, 2012 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You could have used logarithms right from the start- [itex]log(2^{k-2})= log(3^{k+1})[/itex].

    In general, to solve an equation of the form f(x)= constant or f(p(x))= f(q(x)) you will need to use the inverse function to f. And the inverse of the exponential is the logarithm.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Solving Exponential Equations
Loading...