Answers

2015-04-30T09:11:01+05:30
Number of digits in 12^{12} is given by

\left\lfloor\log_{10}12^{12}\right\rfloor+1

=\left\lfloor12\log_{10}(4\times3)\right\rfloor+1

=\left\lfloor12\left(2\log_{10}2+\log_{10}3\right)\right\rfloor+1

=\left\lfloor12\left(2(0.3010)+0.4771\right)\right\rfloor+1

=\left\lfloor12.9492\rfloor+1

=12+1

=13
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