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How can you calculate how many digits are in a number from its index notation?

I need to calculate how many digits are in the number $2^{30} * 5^{25}$

2 Answers 2

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$2^{30}\times5^{25} = 10^{25}\times2^{5} = 32 \times 10^{25}$

Edit

So, there are two digits for 32 and 25 zeros after it. 27 in total.

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    Is that how many digits are in the number though? – 2017-02-25
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    @BeastlyGerbil, see the edit – 2017-02-25
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    Oh I see now, thanks! I'll accept this when possible – 2017-02-25
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For your particular case, $2^{30} \cdot 5^{25} = 2^5\cdot 10^{25}$, which should be straightforward, given that $10^n$ is the smallest number with $n{+}1$ digits.

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    Is that how many digits are in the number though? – 2017-02-25
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    Replace $25$ (in $2^5\cdot 10^{25}$) with small numbers like $1,2,3$ to see the pattern. – 2017-02-25
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    I understand now, thanks! – 2017-02-25