Math  /  Algebra

QuestionALGEBRA II
3. If log(n)=0.6\log (n)=0.6, find the value of log(10n)\log (10 n).
4. If mm is a positive integer and log(m)3.8\log (m) \approx 3.8, how many digits are there in mm ? Explain how you know.
5. If mm is a positive integer and log(m)9.6\log (m) \approx 9.6, how many digits are there in mm ? Explain how you know.
6. Vivian says log(452000)=5+log(4.52)\log (452000)=5+\log (4.52), while her sister Lillian says that log(452000)=6+log(0.452)\log (452000)=6+\log (0.452). Which sister is correct? Explain how you know.

Studdy Solution
Lillian's expression: log(452000)=6+log(0.452)\log (452000) = 6 + \log (0.452).
Rewrite 452000452000 as 0.452×1060.452 \times 10^6:
log(452000)=log(0.452×106)=log(0.452)+log(106)=log(0.452)+6\log (452000) = \log (0.452 \times 10^6) = \log (0.452) + \log (10^6) = \log (0.452) + 6
Lillian is also correct.
The solutions are:
1. log(10n)=1.6\log (10n) = 1.6
2. mm has 4 digits when log(m)3.8\log (m) \approx 3.8.
3. mm has 10 digits when log(m)9.6\log (m) \approx 9.6.
4. Both Vivian and Lillian are correct.

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