log base 3 (4*3^x - 1), log base 9 (3^1-x +2) , 1 are in AP .Find the value of 1-x.
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Therefore, log10 23 < log10 10
or, 3log10 2 < 1
or, log10 2 < 1/3 ................... (i)
Again, 16 > 10 or, 24 > 10
or, log10 24 > log10 10
or, 4 log10 2 > 1
or, log10 2 > 1/4 .................. (ii)
Therefore from (i) and (ii) we get, 1/3 > log10 2 > 1/4
i.e., the value of log10 2 lies between 1/3 and 1/4