41.
If $${\text{a}} = {\text{lo}}{{\text{g}}_{\text{8}}}\,{\text{225}}$$   and $${\text{b = lo}}{{\text{g}}_{\text{2}}}\,{\text{15}},$$   then a in terms of b is -

42.
If $$\log 2 = 0.3010\,$$   and $$\log 3 = 0.4771,\,$$   the value of $${\log _5}512$$   = ?

43.
If the logarithm of a number is - 3.153, what are characteristic and mantissa?

44.
If $$\log 2 = 0.30103,$$    the number of digits in $${4^{50}}$$ is -

45.
The number of digits in $${{\text{4}}^9} \times {{\text{5}}^{17}}{\text{,}}$$   when expressed in usual form, is -

46.
If $$\log 3\log \left( {{3^x} - 2} \right)\,$$   and $$\log \left( {{3^x} + 4} \right)$$   are in arithmetic progression, then x is equal to

47.
If $${\log _{10}}a = p,$$   $${\log _{10}}b = q,$$   then what is $${\log _{10}}\left( {{a^p}{b^q}} \right)$$   equal to?