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    Does anybody know how to solve the question:

    Given that 9^a = 2 , What are the possible values of 27^a ?

    Any help would be highly appreciated. Thanks in advance!

    9 = 3^2
    27 = 3^3
    Hope this helps.

    Log log log

    This can be done one of two ways, usually with this type of question you are supposed to take logs to solve it so, I would take logs of 9^a=2 to the base 2 so log2(9^a)=1 as 2^1=2, now we use laws of logs to get a*log2(9)=1 (* represents multiplication) and then rearrange this, giving a=1/(log2(9)) now you just type 27^(1/(log2(9))) into the calculator and it gives 2.8284... as the answer.
    However as this is a GCSE question and the numbers are nice, it can be done another way, change the 9 and 27 into powers of 3 so we get 3^(2a)=2 and the question is asking for 3^(3a) now if we square root the first one then we reduce the power of 3 so we get 3^a=2^(1/2)=squareRoot(2) now to get 3^(3a) we just need to cube the answer so we get 3^(3a)=27^a=2^(3/4)=squareRoot(2)^3 which gives 2.8284... when entered into the calculator.
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Updated: February 19, 2018
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