Question

find the no. of digits in 5⁵⁰(log5=0.699)​

Answer 1

20

log

10

3=0.477

⇒3=10

0.477

⇒3

40

=10

(0.477)

×40

3

40

=10

0.477×40

=10

19.080

=10

19.1

∴There are 19 digits

Answer 2

Answer:

Let x = 5^{20}5

20

Taking logarithm on both sides

⇒ logx = log 5^{20}5

20

⇒logx = 20log 5

⇒logx = 20(0.699) where log5 = 0.699

⇒logx = 13.98

⇒ The characterstic of x is 13

⇒ The characterstic of 5^{20}5

20

is 13

Therefore, the number of digits in 5^{20}5

20

is 14.