Question

Find the number of digits in 12 to the power 12 if log 2 to the base 10 =0.3010 log 3 to the base 10 =0.4771

Answer 1

Answer:

13

Step-by-step explanation:

number of digits in 12^{12}12

12

is given by

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

10

12

12

⌋+1

=\left\lfloor12\log_{10}(4\times3)\right\rfloor+1=⌊12log

10

(4×3)⌋+1

=\left\lfloor12\left(2\log_{10}2+\log_{10}3\right)\right\rfloor+1=⌊12(2log

10

2+log

10

3)⌋+1

=\left\lfloor12\left(2(0.3010)+0.4771\right)\right\rfloor+1=⌊12(2(0.3010)+0.4771)⌋+1

=\left\lfloor12.9492\rfloor+1

=12+1=12+1

=13=13