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Math Help - Exponential equation

  1. #1
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    Exponential equation

    I can simply do the problem by guess checking but because it is taking far too long, what is the simplest way to do these problems? Examples


    27^4x = 9^x+1

    Thanks~
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by JonathanEyoon View Post
    I can simply do the problem by guess checking but because it is taking far too long, what is the simplest way to do these problems? Examples


    27^4x = 9^x+1

    Thanks~
    get both bases in terms of the same base.

    i assume you mean, 27^{4x} = 9^{x + 1} ?....use parentheses! you should have typed 27^(4x) = 9^(x + 1) if that is the case

    note that 27 = 3^3 and 9 = 3^2

    so we have:

    \left( 3^3 \right)^{4x} = \left(3^2 \right)^{x + 1}

    \Rightarrow 3^{12x} = 3^{2x + 2}

    can you take it from here?
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    get both bases in terms of the same base.

    i assume you mean, 27^{4x} = 9^{x + 1} ?....use parentheses! you should have typed 27^(4x) = 9^(x + 1) if that is the case

    note that 27 = 3^3 and 9 = 3^2

    so we have:

    \left( 3^3 \right)^{4x} = \left(3^2 \right)^{x + 1}

    \Rightarrow 3^{12x} = 3^{2x + 2}

    can you take it from here?

    OHhhhhhhhhhh I totally forgot about base!! Thanks alot and I will use parentheses next time~
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