document.write( "Question 254315: How many digits does 2^15 * 5^8 have when expanded? \n" ); document.write( "

Algebra.Com's Answer #186658 by drk(1908) $\"\"$ $\"About$

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The number of digits in 2^15 = 32768 = 5.
\n" ); document.write( "The number of digits in 5^8 = 390625 = 6.
\n" ); document.write( "multiplied together, we get 11 digits.
\n" ); document.write( "There can be a shortcut but it involves formulas.
\n" ); document.write( "The number of digits of a^b can be approximated by
\n" ); document.write( "(i) N = b*log(a)
\n" ); document.write( "applying the original information, we get
\n" ); document.write( "(ii) 15log(2) ~ 4.515 take the digit and add 1 to get 5.
\n" ); document.write( "(iii) 8log(5) ~ 5.591 take the digit and add 1 to get 6.
\n" ); document.write( "5 + 6 = 11. \n" ); document.write( "

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