46.
The number of digits in $${{\text{4}}^9} \times {{\text{5}}^{17}}{\text{,}}$$   when expressed in usual form, is -

47.
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

48.
If $${\log _{10}}a = p,$$   $${\log _{10}}b = q,$$   then what is $${\log _{10}}\left( {{a^p}{b^q}} \right)$$   equal to?