Use common logarithms or natural logarithms and a calculator

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places log22 339

Solution

log₂₂ 339 = (log 339)/(log 22)         ; since log_b a = (log_c a)/(log_c b)

= (log 3*113)/(log 2*11)  

= (log 3 + log 113)/(log 2 + log11)  

= (1.0986 + 4.727388)/(0.693147 + 2.397895)

= 5.825988 / 3.091042

= 1.884797

= 1.8848

Hence log₂₂ 339 = 1.8848