LOGARITHMS 1B

Evaluate Log100000 +  log 0.00001 + log₃243

Solution

= Log100000 +  log 0.001 + log₃243

= Log10⁵ +  log 10^-5 + log₃3⁵

= 5Log10 +  (-5log 10) + (5log₃3)    [since log_aaⁿ  = nlog_aa]

= (5x1) + (-5x1) + (5x1)            [since log_aa = 1]

= 5 + (-5) + (5)

= 5

Hence Log100,000 +  log 0.00001 + log₃243 = 5

TRY THIS...............................

Evaluate Log10,000,000 +  log 0.01 + log₃729