Question

find the number of digits in 12power12 if log2=0.3010 and log3=0.4771

Answer 1

number of digits in $12^{12}$ is given by

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

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

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

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

$=\left\lfloor12.9492\rfloor+1$

$=12+1$

$=13$