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$\log_2 X$, $\log_2 (X+9)$ and $\log_2(X+45)$ are 3 consecutive terms of an arithmetic progression; find

$\qquad$(i) the value of X;
$\qquad$(ii) the first term and the common difference; and
$\qquad$(iii) the 5th term as a single logarithm.

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    to begin with: do you mean $log_{2}X, log_{2}(x+9), log_{2}(x+45)$ or $log(2^x), log(2^{x+9}), log(2^{x+45})$? clarify it please so that the problem can be solved.2012-01-05
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    I’ve edited it into the form that you actually wrote; is that what you intended, or did you want $\log_2 X$, $\log_2 (X+9)$, and $\log_2 (X+45)$?2012-01-05
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    Never mind: the problem makes no sense unless I reinterpret it with logs base $2$, so I’ve changed the edit.2012-01-05
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    @BrianM.Scott. I think this will not work since you get $X\log 2-(X+9)\log 2=(X+9)\log 2-(X+45)\log 2$ which is false as you can check. Maybe he means the second one.2012-01-05
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    Must be second, $X=3$.2012-01-05

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