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If the value of an article is assumed to increase annually by 5% of its value at the beginning of the year, after how many years will its value double.

Here is what I've done so far: Value at beginning of year = x, number of years = n, r = 1.05 x[1.05^(n-1)] = 2x

How do I solve for n?

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    $\begingroup$ This means that $(1.05)^{n-1} = 2$. Have you learnt about logarithms yet? $\endgroup$
    – Mathmo123
    Commented Jul 20, 2014 at 10:06
  • $\begingroup$ It is $1.05^n$. $\endgroup$
    – André Nicolas
    Commented Jul 20, 2014 at 10:11
  • $\begingroup$ If the word "logarithm" does not ring any bells to you, the only way to solve it is trial and error. On a pocket calculator (the kind that might be solar powered), type 1.5 and hit the multiply button twice. Then see how many times you need to press the $=$-button to get past $2$. $\endgroup$
    – Arthur
    Commented Jul 20, 2014 at 10:16

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Your progress so far is correct. $x1.05^{n-1} = 2x$ implies that (dividing by $x$ on both sides): $$1.05^{n-1} = 2$$

Taking the logarithm of both sides yields:

$$(n-1)\log(1.05) = \log(2)$$

Can you take it from here?

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