Without using log table, prove the following:
i)
ii)
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Answer:
1/4 < log2 < 1/3
1/3 < log 3 < 1/2
Step-by-step explanation:
To be proved
1/4 < log2 < 1/3
take one by one
1/4 < log2
if 1 < 4 log 2
if log 10 < log 2⁴
if log 10 < log 16
which is true
hence
1/4 < log2
log2 < 1/3
if 3log2 < 1
if log 2³ < log 10
if log 8 < log 10
which is true
Hence
1/4 < log2 < 1/3
correct Question is :
1/3 < log 3 < 1/2
1/3 < log 3
if 1 < 3 log 3
if log 10 < log 3³
if log 10 < log 27
which is true
log 3 < 1/2
if 2log3 < 1
if log 3² < log 10
if log 9 < log 10
which is true
hence
1/3 < log 3 < 1/2
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