3/10 < log10 (2) < 1/3
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Ishitaa1:
we gotta prove that without using log table
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y1 = lg2 -3/10 y2=lg2- 1/3
= 3*lg2 - lg10^3 =3*lg2 - lg10
=lg2^3 - lg1000 =lg8/10
= lg(8/1000)
z =y2 - y1
= lg(8/10) - lg(8/1000)
= lg(1000/10)
=lg100
=lg10^2
=2
accordingly y2 - y1>0
y2>y1
= 3*lg2 - lg10^3 =3*lg2 - lg10
=lg2^3 - lg1000 =lg8/10
= lg(8/1000)
z =y2 - y1
= lg(8/10) - lg(8/1000)
= lg(1000/10)
=lg100
=lg10^2
=2
accordingly y2 - y1>0
y2>y1
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