Question

Evaluate the following without using tables :
log 4 + `1/3` log 125 - `1/5`log 32 

Answer 1

Consider the given expression
log 4 + `1/3"log 125" - 1/5` log 32

= `log 4 + log ( 125 )^(1/3) - log(32)^(1/5)`     ...[ nlog_am = log_amⁿ ]

= `log 4 + log(5^3)^(1/3) - log(2^5)^(1/5)`

= log 4 + log 5 - log 2
= log 4 x 5 - log 2                ....[ log_am + log_an = log_amn] 
= `"log"(20/2)                    .....[ log_am - log_an = log_a(m/n)]`
= log 10
= 1