Question

1. If log 2 log 3 log 4 x = 1, find the number of digits in x.
[log 2 = 0.3010]​

Answer 1

Step-by-step explanation:

ANSWER

log2000

2000

=2000log2000=2000log(2×10

3

)

=2000[log2+3log10]

=2000[0.30103+(3×1)]

=6602.06

x=6602.06

When we take log with base 10, integer in answer shows one less than number of digits in number.

So, number of digits in number 2000

2000

=6602+1=6603

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Answer 2

Answer:

6

Step-by-step explanation:

log2(log3(log4(x)))=1

log3(log4(x))=2

log4(x)=3²=9

x=4⁹=2¹⁸

as log(2)=0.3010

18*0.3010=5.418

characteristic length=5

no of digits is 6

alternative..

4⁹=262144

so 6 digits