A-Math: Solving Indices Equation (Involving Common Base)

This topic is taught in Secondary 3 after introduction of Indices Law.

In solving indices equation involving the same base, one of the common techniques is by Substitution. But before you can do substitution, you need to apply indices law to 'break down' the equation. This process of breaking down is sometimes challenging for students. Knowing how to solve quadratic equation is also essential.

Sometimes, solving Indices Equation will also involve the concept of taking lg on both sides as well.

In the following example, you will Substitution and 'Breaking down' in action:


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E-Maths: How to Solve Indices Equations (Video) Length of video: 4 mins. Direct link to video: http://www.youtube.com/watch?v=UHgEW5WiGh8 Leave your answer for bonus question in the comments s...

Hi, I'm Ai Ling Ong. I enjoy coaching students who have challenges with understanding and scoring in 'O' Level A-Maths and E-Maths. I develop Math strategies, sometimes ridiculous ideas to help students in understanding abstract concepts the fast and memorable way. I write this blog to share with you the stuff I teach in my class, the common mistakes my students made, the 'way' to think, analyze... If you have found this blog post useful, please share it with your friends. I will really appreciate it! :)

24 Responses to A-Math: Solving Indices Equation (Involving Common Base)

  1. how would you solve this if ^ means to the power of-


    j hate Reply:

    with 2 unknowns you need 2 equations to solve for the unknowns


  2. no root exist

    Possible derivation:
    d/dp(4^(p-3) 7^(q-1))
    | Factor out constants:
    = | 7^(q-1) (d/dp(4^(p-3)))
    | Use the chain rule, d/dp(4^(p-3)) = ( d4^u)/( du) ( du)/( dp), where u = p-3 and ( d4^u)/( du) = 4^u log(4):
    = | 7^(q-1) (4^(p-3) log(4) (d/dp(p-3)))
    | Differentiate the sum term by term:
    = | 4^(p-3) 7^(q-1) log(4) (d/dp(p)+d/dp(-3))
    | The derivative of -3 is zero:
    = | 4^(p-3) 7^(q-1) log(4) (d/dp(p)+0)
    | The derivative of p is 1:
    = | 1 4^(p-3) 7^(q-1) log(4)


  3. solve for x and y


    Praveen Reply:

    Sounds and looks complicated but actually not too bad once we see the trick. Maybe the qn should include the additional stipulation that x and y are integers.

    Then, by simple trial and error, x and y are 2 and 3 (Either way).

    Nice qn.


  4. pls solve X^2=16^X for me


    Ai Ling Reply:

    May I know which grade you are?


    Praveen Reply:

    Interesting qn Rahim.

    The answer is -0.5 I believe. You can either use graphing calculator or 'trial and error' method. I don't think you can do such questions using conventional logarithmic techniques.

    If the qn were slightly modified, example x^2=3^x, and you are not allowed to use graphing calculator, then may need to rely on more advanced techniques such as Newton-Raphson method.

    Comments and sharing are welcome.



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