1/4loga^3+5log^b=1 find a^3b^10 value
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We have, 8 < 10 or, 2³ < 10
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
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
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