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    Hello. I was looking through an AQA GCSE past paper and the last question on the paper was this:

     3^x = 9^{x + 1}

    Solve  x

    I was wondering if someone could explain the process of solving an equation like this.
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    can you write the right hand side so that is also has a base of 3?
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    (Original post by xy_)
    Hello. I was looking through an AQA GCSE past paper and the last question on the paper was this:

     3^x = 9^{x + 1}

    Solve  x

    I was wondering if someone could explain the process of solving an equation like this.
    If you have two numbers, like 5^a and 5^b and they are equal (5^a = 5^b) then what can you say about a and b?

    And how does this relate to your example, and how is it different?
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     9^{x+1} = (3^2)^{x+1} = (3^{x+1})^2 .
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    (Original post by xy_)
    Hello. I was looking through an AQA GCSE past paper and the last question on the paper was this:

     3^x = 9^{x + 1}

    Solve  x

    I was wondering if someone could explain the process of solving an equation like this.

    aren't these exponential equations?
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    Ah, I see. So:

    

3^x = 9^{x+1}

3^x = (3^2)^{x+1}

3^x = 3^{2x+2}

x = 2x+2

x - 2 = 2x

-2 = x

    Thanks for the help - if the above is correct then it all makes much more sense!
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    (Original post by SeanFM)
    If you have two numbers, like 5^a and 5^b and they are equal (5^a = 5^b) then what can you say about a and b?

    And how does this relate to your example, and how is it different?
    So a and b must be the same? So getting the same base means the exponents equal each other. So then with the same base I can divide by the base and just solve the equation left by the exponents.
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    (Original post by xy_)
    So a and b must be the same? So getting the same base means the exponents equal each other. So then with the same base I can divide by the base and just solve the equation left by the exponents.
    Almost correct - just to be pernickety, you can't 'divide' by the base - they disappear as you 'compare' the exponents as they must be equal, like you've said . but well done for figuring out so much from just one small hint
 
 
 
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