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I know basics of logarithm. I encountered this problem in my maths book.I don't know how to find number of digits in the problem. Please help me.

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    $2^{56} = 10^{56 \log 2}$ – Thomas Sep 02 '17 at 08:25
  • Can it give me number of digits in it. –  Sep 02 '17 at 08:27
  • Note that it is obvious from the above hint that: $$10^{16}<10^{56\log(2)}<10^{17}$$ How many digits are in $10^{16}$, and how many digits are in $10^{17}$? Now deduce the number of digits in $10^{56\log(2)}$. – projectilemotion Sep 02 '17 at 08:37
  • How many digits are in $10^1$? How many digits are in $10^2$? How about any exponent between $1$ and $2$? What about larger exponents? – Arthur Sep 02 '17 at 08:39

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Given that $2= 10^{\log_{10} 2}$, then $2^{56}=(10^{\log_{10} 2})^{56}=10^{56\log2}$.

Now simply substitute your given $\log2$ into the equation:

$2^{56}=10^{56 \times 0.30103}=10^{16.85768}$

Therefore it is clear your answer will be $16+1=17$ digits.

anonymous
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