Find the smallest positive integer k such that the baseten representation of 3k has exactly one hundred digits. If log_(8)3=p and log_(3)5=q, then, in terms of p and q log_(5) equals to?

tashiiexb0o5c

tashiiexb0o5c

Answered question

2022-09-04

Find the smallest positive integer k such that the baseten representation of 3k has exactly one hundred digits.
If log 8 3 = p   a n d   log 3 5 = q , then, in terms of p and q, log 5 equals to?

Answer & Explanation

Maggie Tanner

Maggie Tanner

Beginner2022-09-05Added 18 answers

3 k = 10 100
log ( 3 k ) = log ( 10 100 )
k log 3 = 100
k = 100 / log 3 = 209.6
nearest integer =210 ( 3 k will be 1.56842404 × 10 100 )
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For the second problem, is log 5 supposed to be in base 10?
If so, you need touse:
p = ( log 10 3 ) / ( log 10 8 )
q = ( log 10 5 ) / ( log 10 3 )

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