Without using your calculator find out which one is bigger l

Without using your calculator, find out which one is bigger log_23 or log_854

Solution

The formula for change of base in logarithms is log_a(x) = log_b(x)/ log_b(a). Thus, if a = 2 , b = 8 and x = 3, then, log₂ (3) = log₈(3)/log₈(2). Also, log₈(54) = log₈(3³ * 2) = log₈(3³) + log₈(2) = 3log₈(3) + log₈(2) . (as log xy) = logx + log y ang logp^q = qlogp).

Now it is apparent that log₈54 is bigger than log₂3.